Every \command in the LaTeX universe, explained

This page defines every LaTeX command and environment that appears in any lesson on Oleafly Learn, plus the wider standard vocabulary you will meet in real papers: the kernel, amsmath, hyperref, graphicx, booktabs, biblatex, TikZ, Beamer, and the packages researchers actually load. Skim it by category, or search the page with Ctrl/Cmd-F for the command you just met. Each entry is one line: what it does and, where it matters, which package it comes from.

Document classes and setup

Command	What it does
\documentclass{article}	First line of every document: picks the overall layout; article is the default choice for papers.
\documentclass{report}	Class for longer reports: adds \chapter and starts the abstract on its own page.
\documentclass{book}	Class for books: chapters, two-sided layout, front/main/back matter.
\documentclass{letter}	Class for correspondence, with \opening, \closing, and address commands.
\documentclass{beamer}	Class for slide presentations built from frame environments.
\documentclass[11pt,a4paper]{article}	Common class options: font size (10pt, 11pt, 12pt), paper (a4paper, letterpaper), twocolumn, twoside, landscape, draft, titlepage.
\usepackage{amsmath}	Loads a package in the preamble to add features.
\usepackage[margin=1in]{geometry}	Sets page margins and paper size (geometry).
\title{...}	Stores the document title, printed later by \maketitle.
\author{...}	Stores the author list for \maketitle; separate multiple authors with \and.
\and	Separator between author names inside \author{...}.
\date{...}	Stores the date shown by \maketitle; \date{} hides it, \date{\today} shows today.
\today	Prints the current date at compile time.
\maketitle	Prints the title block from \title, \author, and \date.
\thanks{...}	Attaches a footnote to a title or author name, e.g. for funding or contact info.
\institute{...}	Author affiliation command used by Beamer and the Springer LNCS class.
\inst{1}	Affiliation superscript marker in LNCS and Beamer author lists: Ada Lovelace\inst{1}.
\keywords{...}	Prints the paper’s keyword list in publisher classes like acmart and llncs.
\address{...}	letter class: stores the sender’s address for the letterhead.
\signature{...}	letter class: stores the name printed under the closing.
\opening{Dear ...}	letter class: prints the salutation and starts the letter body.
\closing{Sincerely,}	letter class: prints the sign-off and signature block.
\LaTeX	Prints the LaTeX logo with its raised and lowered letters.
\TeX	Prints the TeX logo with its lowered E.
\input{file}	Pastes another .tex file in place, as if you had typed it there.
\include{chapter1}	Inputs a chapter file starting on a new page; enables partial compiles via \includeonly.
\includeonly{chapter1,chapter3}	Preamble list restricting which \include files actually compile.
\hypersetup{...}	Configures hyperref options such as link colors and PDF metadata.
\AtBeginDocument{...}	Runs code right after \begin{document}, useful for late setup.
\AtEndDocument{...}	Runs code just before the document ends.
\makeatletter	Temporarily makes @ a letter so you can use or patch internal commands.
\makeatother	Restores @ to normal after \makeatletter.
\typeout{...}	Prints a message to the compile log and terminal, handy for debugging.
\protect	Shields a fragile command inside a moving argument like \caption or \section.
\listfiles	Preamble command that logs every loaded file and its version, for bug reports.

Structure and sectioning

Command	What it does
\part{...}	Highest-level division, above chapters, in book and report classes.
\chapter{...}	Numbered chapter heading in book and report classes (not in article).
\section{...}	Numbered top-level heading in an article.
\subsection{...}	Numbered heading one level below \section.
\subsubsection{...}	Numbered heading one level below \subsection.
\paragraph{...}	Lowest-level heading: a run-in bold title at the start of a paragraph.
\subparagraph{...}	One level below \paragraph, rarely needed.
\section*{...}	Starred sectioning prints the heading without a number or TOC entry.
\appendix	Switches numbering so the following chapters or sections become Appendix A, B, C.
\appendixpage	Prints a separate “Appendices” divider page (appendix package).
\tableofcontents	Prints the table of contents, built from your sectioning commands.
\listoffigures	Prints a list of all figure captions with page numbers.
\listoftables	Prints a list of all table captions with page numbers.
\frontmatter	Book-class switch for the pre-content pages: roman page numbers, unnumbered chapters.
\mainmatter	Book-class switch back to the main content: arabic page numbers, numbered chapters.
\backmatter	Book-class switch for the end pages: chapters stop being numbered.
\addcontentsline{toc}{chapter}{...}	Manually adds an entry to the table of contents (or a list of figures/tables).
\addtocontents{toc}{...}	Writes arbitrary material (like spacing) into a contents file.
\setcounter{secnumdepth}{3}	Controls how deep sectioning numbers go.
\setcounter{tocdepth}{2}	Controls how deep the table of contents goes.

Defining commands and environments

Command	What it does
\newcommand{\R}{\mathbb{R}}	Defines your own command; errors if the name already exists.
\renewcommand{...}{...}	Redefines an existing command; errors if it does not exist.
\providecommand{...}{...}	Defines a command only if it is not already defined; otherwise silently does nothing.
\NewDocumentCommand	Modern command definition with flexible optional arguments (LaTeX3/xparse).
\newenvironment{name}{begin code}{end code}	Defines your own environment with code run at \begin and \end.
\renewenvironment{name}{...}{...}	Redefines an existing environment.
\ensuremath{...}	Makes a macro’s math content work both inside and outside math mode.
\DeclareMathOperator{\E}{E}	Defines an upright operator name; the starred form puts limits below (amsmath).
\DeclareMathOperator*{\argmin}{arg\,min}	Starred form: the operator takes limits below in display math (amsmath).
\newtheorem{lemma}{Lemma}	Declares a theorem-like environment (amsthm).
\foo	Example name for a user-defined macro in the \newcommand lesson, not a real LaTeX command.
\abs{x}	Example user-defined macro from the custom commands lesson that typesets absolute-value bars.
\mat{A}	Example user-defined macro from the custom commands lesson for a bold matrix symbol.
\vect{v}	Example user-defined macro from the custom commands lesson for a bold vector symbol.
\set{...}	Example user-defined macro from the custom commands lesson that typesets sized set braces.
\citepair	Example user-defined citation helper macro from the custom commands lesson, not a standard command.
\E	Example user-defined operator for expectation, typically defined with \DeclareMathOperator or \newcommand.
\R	Example user-defined macro for the reals: \newcommand{\R}{\mathbb{R}}.
\argmax, \argmin	Operator names for arg max / arg min, defined in this course with \DeclareMathOperator* so subscripts sit below.

Counters and lengths

Command	What it does
\newcounter{examples}	Creates a new counter, optionally reset by a parent: \newcounter{examples}[section].
\setcounter{page}{1}	Sets a counter’s value, here restarting page numbers.
\addtocounter{examples}{2}	Adds a value to a counter without printing anything.
\stepcounter{examples}	Increments a counter by one.
\refstepcounter{examples}	Increments a counter and makes it the target for the next \label.
\value{examples}	Reads a counter’s value for use in arithmetic or comparisons.
\arabic{examples}	Prints a counter as arabic numerals: 1, 2, 3.
\roman{examples}, \Roman{examples}	Prints a counter as lowercase or uppercase roman numerals.
\alph{examples}, \Alph{examples}	Prints a counter as lowercase or uppercase letters.
\fnsymbol{footnote}	Prints a counter as footnote symbols: asterisk, dagger, and so on.
\newlength{\mygap}	Creates a new length register.
\setlength{\parskip}{6pt}	Assigns a value to a length register.
\addtolength{\textheight}{1cm}	Adds to an existing length.
\settowidth{\mygap}{text}	Sets a length to the natural width of some text.
\parindent	Length of the first-line paragraph indent; set with \setlength{\parindent}{0pt}.
\parskip	Length of the vertical gap between paragraphs; set with \setlength.
\linewidth	Length of the current line, handy for sizing: width=\linewidth.
\textwidth	Length of the full text block width on the page.
\textheight	Length of the full text block height on the page.
\columnwidth	Width of one column in a multi-column layout.
\baselineskip	Vertical distance between baselines of consecutive lines.
\linespread{1.3}	Scales the leading (line spacing) for the whole document; needs \selectfont or a size command to take effect in place.

Paragraphs, line breaks, and hyphenation

Command	What it does
\\	Ends the current line inside paragraphs, tables, and arrays.
\\[6pt]	Line break with extra vertical space after it.
\newline	Breaks the line without justifying it and without allowing a page break.
\linebreak	Requests a justified line break here; optional [0-4] sets insistence.
\nolinebreak	Discourages a line break at this point.
\par	Ends the paragraph, same as a blank line in the source.
\noindent	Suppresses the first-line indent of the paragraph that follows.
\indent	Forces the first-line indent where it would otherwise be suppressed.
\-	Marks an allowed hyphenation point inside a word.
\hyphenation{data-set}	Preamble list teaching LaTeX how to hyphenate specific words.
\sloppy	Loosens spacing rules so lines break more easily, avoiding overfull boxes.
\fussy	Restores strict spacing rules after \sloppy.
\raggedright	Left-aligns the following text instead of justifying it.
\raggedleft	Right-aligns the following text.
\centering	Centers everything that follows inside the current group, e.g. a figure’s image.
\samepage	Discourages page breaks within the current group.
\enlargethispage{\baselineskip}	Makes only the current page a bit taller, to squeeze in one more line.
~	Non-breaking space: Figure~1 keeps the number on the same line.

Spacing

Command	What it does
\quad	Inserts a horizontal space about the width of a capital M.
\qquad	Inserts twice the space of \quad.
\enspace	Inserts half a \quad of horizontal space.
\hspace{1cm}	Inserts horizontal space; disappears at a line break.
\hspace*{1cm}	Horizontal space that survives even at a line break.
\vspace{1cm}	Inserts vertical space of a given length.
\vspace*{1cm}	Vertical space that survives even at a page break.
\smallskip	Inserts a small vertical gap between paragraphs.
\medskip	Inserts a medium vertical gap between paragraphs.
\bigskip	Inserts a large vertical gap between paragraphs.
\hfill	Stretchy horizontal space that pushes content apart to fill the line.
\vfill	Stretchy vertical space that pushes content apart to fill the page.
\dotfill	Fills the remaining line with dots, as in a menu or contents line.
\hrulefill	Fills the remaining line with a horizontal rule.
\stretch{2}	Stretchy glue with a weight, for proportional spacing: \hspace{\stretch{2}}.
\fill	The unit stretchy length; \hspace{\fill} is what \hfill expands to.
\phantom{text}	Takes up exactly the space of its argument but prints nothing.
\hphantom{text}	Takes up only the width of its argument, with zero height.
\vphantom{text}	Takes up only the height of its argument, with zero width.
\smash{...}	Prints its argument but pretends it has zero height and depth.
\strut	Invisible support the height of a normal line, to even out row heights.
\mathstrut	Math-mode strut the size of a parenthesis, to align radicals and fractions.

Boxes and rules

Command	What it does
\mbox{...}	Unbreakable horizontal box; also keeps its contents on one line.
\makebox[3cm][r]{...}	Box of a set width with chosen alignment (l, c, r, s).
\fbox{...}	Draws a frame around its contents.
\framebox[3cm][c]{...}	Framed box of a set width with chosen alignment.
\parbox{5cm}{...}	A paragraph box: a mini column of text of the given width.
\raisebox{2pt}{...}	Shifts its contents up (or down with a negative length).
\rule{2cm}{0.4pt}	Draws a filled rectangle; the workhorse for custom lines.
\colorbox{yellow}{...}	Puts text on a colored background box (xcolor).
\fcolorbox{red}{yellow}{...}	Colored box with a colored frame (xcolor).

Pages, numbering, and headers

Command	What it does
\newpage	Ends the current page and starts a new one.
\clearpage	Starts a new page after first flushing all pending figures and tables.
\cleardoublepage	Like \clearpage but also ensures the next page is a right-hand (odd) page.
\pagebreak	Requests a page break at this point, stretching the page to full height.
\nopagebreak	Discourages a page break at this point.
\pagenumbering{roman}	Sets the page number style (arabic, roman, Roman, alph, Alph), resetting the counter to 1.
\pagestyle{fancy}	Sets the running header/footer style (plain, empty, headings, myheadings, fancy) for all following pages.
\thispagestyle{empty}	Overrides the header/footer style for the current page only.
\thepage	Prints the current page number; used inside headers and footers.
\marginpar{...}	Puts a note in the page margin next to the current line.
\fancyhf{}	Clears all fancyhdr header and footer fields before setting your own.
\fancyhead[R]{...}	Sets a fancyhdr header field, here the right-hand one.
\fancyfoot[C]{\thepage}	Sets a fancyhdr footer field, here a centered page number.
\headrulewidth	fancyhdr macro for the header rule thickness; renew to 0pt to remove the line.
\footrulewidth	fancyhdr macro for the footer rule thickness, 0pt by default.
\newgeometry{margin=2cm}	Changes page geometry mid-document (geometry).
\restoregeometry	Returns to the preamble geometry after \newgeometry (geometry).

Special characters

The ten reserved characters and how to print them, plus common text symbols.

Command	What it does
\%	Prints a percent sign (bare % starts a comment).
\&	Prints an ampersand (bare & is the table column separator).
\#	Prints a hash (bare # marks macro arguments).
\_	Prints an underscore (bare _ is a math subscript).
\{ and \}	Print curly braces (bare braces group).
\$	Prints a dollar sign (bare $ toggles math mode).
\textbackslash	Prints a backslash in text.
\textasciitilde	Prints a tilde in text (bare ~ is a non-breaking space).
\textasciicircum	Prints a caret in text (bare ^ is a math superscript).
\textbar	Prints a vertical bar in text.
\textless, \textgreater	Print < and > correctly in text mode.
\ldots, \dots	Ellipsis with correct spacing; \dots adapts in math mode (amsmath).
\textellipsis	The text-mode ellipsis that \dots uses outside math.
\textemdash, \textendash	Named commands for the em and en dash (same output as --- and --).
\textquotedblleft, \textquotedblright	Curly double quotation marks (usually typed as backtick pairs and apostrophe pairs).
\guillemetleft, \guillemetright	French angle quotation marks (older spelling: \guillemotleft/\guillemotright).
\dag, \ddag	Dagger and double dagger in text, common for author affiliations.
\S	Section sign, as in S 2.1 of a legal document.
\P	Paragraph (pilcrow) sign.
\pounds	British pound sign.
\euro	Euro sign (eurosym package; the kernel also provides \texteuro).
\copyright	Copyright sign.
\textregistered	Registered trademark sign.
\texttrademark	Trademark sign.
\textdegree	Degree sign: 25\textdegree C.
\textmu	Upright micro sign for text like microns.
\textperthousand	Per-mille sign.

Accents and special letters

For pdfLaTeX-era text accents; with XeLaTeX/LuaLaTeX and UTF-8 input you can usually just type the character.

Command	What it does
\'{e}	Acute accent: e-acute as in cafe with an accent.
\`{e}	Grave accent.
\^{o}	Circumflex accent.
\"{u}	Umlaut/dieresis.
\~{n}	Tilde accent, as in Spanish n-tilde.
\c{c}	Cedilla, as in French c-cedilla.
\v{s}	Caron (hacek), common in Czech and Croatian names.
\H{o}	Hungarian double acute accent.
\k{a}	Ogonek, as in Polish a-ogonek.
\b{o}	Bar-under accent.
\d{u}	Dot-under accent, used in transliteration.
\r{a}	Ring accent, as in Scandinavian a-ring.
\u{o}	Breve accent.
\.{o}	Dot-over accent.
\t{oo}	Tie accent joining two letters.
\i, \j	Dotless i and j, for stacking accents: \'{\i}.
\ae, \AE	The ae ligature, lowercase and uppercase.
\oe, \OE	The oe ligature, as in French oeuvre.
\ss	German sharp s (eszett).
\o, \O	Slashed o, as in Danish and Norwegian names.
\l, \L	Polish slashed l.
\aa, \AA	A-ring as a standalone letter, as in Angstrom’s name.

Fonts and sizes

Command	What it does
\textbf{...}	Bold text.
\textit{...}	Italic text.
\emph{...}	Emphasis that adapts to context: italic in upright text, upright in italic text.
\textsc{...}	Small caps text.
\texttt{...}	Typewriter (monospace) text, good for code and filenames.
\textrm{...}	Roman (serif) family text.
\textsf{...}	Sans-serif family text.
\textmd{...}	Medium (normal) weight, undoing bold.
\textup{...}	Upright shape, undoing italic or slanted.
\textsl{...}	Slanted (oblique) shape, distinct from true italic.
\textnormal{...}	Resets to the document’s default font in one step.
\underline{...}	Underlines text; use sparingly, emphasis is usually \emph.
\rmfamily, \sffamily, \ttfamily	Declarations switching the font family (serif, sans, mono) until the group ends.
\bfseries, \mdseries	Declarations switching to bold or back to medium weight.
\itshape, \slshape, \scshape, \upshape	Declarations switching shape: italic, slanted, small caps, upright.
\normalfont	Declaration resetting family, series, and shape to the defaults.
\em	Declaration form of \emph: {\em like this}.
\tiny	Smallest of the ten size commands.
\scriptsize	Second smallest size, roughly subscript sized.
\footnotesize	The size used for footnotes.
\small	Slightly smaller than normal.
\normalsize	The document’s base size.
\large, \Large, \LARGE	One, two, and three steps larger than normal.
\huge, \Huge	The two largest standard sizes.
\fontsize{14}{17}\selectfont	Sets an arbitrary font size and baseline skip, then activates it.
\selectfont	Activates pending font attribute changes (NFSS).
\textsuperscript{...}	Raised small text, as in 1st or footnote-style markers.
\textsubscript{...}	Lowered small text in text mode.
\familydefault	Macro holding the default font family; renew it to change the whole document’s font.
\sfdefault	Macro naming the sans-serif family; \renewcommand{\familydefault}{\sfdefault} makes the document sans.
\setmainfont{...}	Sets the main body font by name under XeLaTeX or LuaLaTeX (fontspec).
\setsansfont{...}	Sets the sans-serif font by name under XeLaTeX or LuaLaTeX (fontspec).
\setmonofont{...}	Sets the monospace font by name under XeLaTeX or LuaLaTeX (fontspec).

Color (xcolor)

Command	What it does
\textcolor{red}{...}	Colors a piece of text.
\color{blue}	Declaration form: colors everything until the group ends.
\definecolor{brand}{HTML}{2F6F4F}	Defines a named color for later use.
\pagecolor{gray!10}	Sets the background color of the whole page.
\rowcolor{gray!20}	Colors one table row (xcolor with the table option, via colortbl).
\cellcolor{gray!20}	Colors one table cell (colortbl).
\rowcolors{2}{gray!10}{white}	Alternating row colors starting at a given row (xcolor table option).

Graphics (graphicx)

Command	What it does
\includegraphics[width=\linewidth]{plot.pdf}	Inserts an image file; key options: width, height, scale, angle, trim+clip, page.
\graphicspath{{figures/}}	Tells LaTeX which folders to search for image files.
\rotatebox[origin=c]{90}{...}	Rotates its contents by an angle.
\scalebox{0.8}{...}	Scales its contents by a factor.
\resizebox{5cm}{!}{...}	Resizes contents to a target width and/or height; ! keeps the aspect ratio.
\reflectbox{...}	Mirrors its contents horizontally.
\includepdf[pages=-]{paper.pdf}	Inserts whole pages from another PDF (pdfpages).

Entering math mode

Command	What it does
$...$	Inline math within a sentence.
\(...\)	LaTeX’s official inline math delimiters, equivalent to $...$.
\[...\]	Unnumbered displayed equation on its own line.
$$...$$	Plain TeX display math; discouraged in LaTeX, use \[...\] instead.
x^2, x_i	^ makes superscripts and _ makes subscripts; brace multi-character scripts: x^{10}.

Math: Greek letters

All of these work only in math mode. Uppercase forms exist where the Greek capital differs from the Latin one.

Command	What it does
\alpha \beta \gamma \delta	Greek letters alpha, beta, gamma, delta.
\epsilon \zeta \eta \theta	Greek letters epsilon, zeta, eta, theta.
\iota \kappa \lambda \mu \nu	Greek letters iota, kappa, lambda, mu, nu.
\xi \pi \rho \sigma \tau	Greek letters xi, pi, rho, sigma, tau.
\upsilon \phi \chi \psi \omega	Greek letters upsilon, phi, chi, psi, omega.
\Gamma \Delta \Theta \Lambda \Xi \Pi	Uppercase Greek letters Gamma through Pi.
\Sigma \Upsilon \Phi \Psi \Omega	Uppercase Greek letters Sigma through Omega.
\varepsilon \vartheta \varpi	Variant forms of epsilon (the curly one most papers use), theta, and pi.
\varrho \varsigma \varphi	Variant forms of rho, sigma (word-final), and phi (open curly).
\varGamma \varDelta \varTheta \varLambda	Italic uppercase Greek variants (amsmath).
\varXi \varPi \varSigma \varUpsilon \varPhi \varPsi \varOmega	The remaining italic uppercase Greek variants (amsmath).

Math: binary operators

Command	What it does
\pm, \mp	Plus-minus and minus-plus signs.
\times	Multiplication cross, also used for dimensions like 3 x 3.
\div	Division (obelus) sign.
\cdot	Centered dot for multiplication.
\ast, \star, \bullet, \circ	Asterisk, star, bullet, and small-circle operators; \circ is also function composition.
\oplus, \ominus	Circled plus (direct sum, XOR) and circled minus.
\otimes, \oslash, \odot	Circled times (tensor product), circled slash, circled dot.
\wedge, \vee	Wedge (logical AND, exterior product) and vee (logical OR, join).
\land, \lor	Aliases of \wedge and \vee named for their logical reading.
\cap, \cup	Set intersection and union signs.
\setminus	Set difference backslash: A \setminus B.
\uplus	Union with a plus, for multiset or disjoint union.
\sqcap, \sqcup	Square cap and cup, meet and join in lattice theory.
\amalg	Amalgamation (upside-down product), used for coproducts.
\dagger, \ddagger	Dagger and double dagger as math operators, e.g. conjugate transpose A^\dagger.
\bigtriangleup, \bigtriangledown	Triangle operators, e.g. symmetric difference.
\triangleleft, \triangleright	Sideways triangles, e.g. normal subgroup relation.

Math: relations

Command	What it does
\leq, \le	Less-than-or-equal sign (\le is the short alias).
\geq, \ge	Greater-than-or-equal sign (\ge is the short alias).
\neq, \ne	Not-equal sign (\ne is the short alias).
\ll, \gg	Much-less-than and much-greater-than signs.
\approx	Approximately-equal sign.
\sim	Tilde relation, read as ‘is distributed as’ or ‘is similar to’.
\simeq	Asymptotically-equal sign (tilde over equals).
\cong	Congruent-to sign (tilde over two bars), used for isomorphism.
\equiv	Identical-to (triple bar) sign, also used for congruence.
\propto	Proportional-to sign.
\asymp	Asymptotically-equivalent relation (stacked curves).
\doteq	Equals sign with a dot, read as ‘approaches’ or ‘is defined as’.
\prec, \succ	Precedes and succeeds relations, curved orderings.
\preceq, \succeq	Precedes-or-equals and succeeds-or-equals.
\subset, \subseteq	Proper subset and subset-or-equal signs.
\supset, \supseteq	Proper superset and superset-or-equal signs.
\sqsubseteq, \sqsupseteq	Square subset and superset relations, used for information order.
\in, \notin	Set membership and its negation: x \in A.
\ni	Reversed membership: the set contains the element.
\vdash, \dashv	Turnstile ‘proves’ and its reverse.
\models	Double turnstile, semantic entailment.
\perp	Perpendicular / independence relation.
\parallel	Parallel bars relation.
\mid	Vertical bar with relation spacing, as in set-builder notation or ‘divides’.
\not	Negates the following relation by overprinting a slash: \not\subset.

Math: arrows

Command	What it does
\to, \rightarrow	Right arrow, as in function types f: A \to B and limits x \to 0.
\gets, \leftarrow	Left arrow, also used for assignment in pseudocode.
\leftrightarrow	Two-headed single arrow.
\Rightarrow	Double right arrow, read as ‘implies’.
\Leftarrow	Double left arrow, read as ‘is implied by’.
\Leftrightarrow	Double two-headed arrow, read as ‘if and only if’.
\implies, \impliedby	Spaced-out \Rightarrow and \Leftarrow for logic (amsmath).
\iff	Spaced-out \Leftrightarrow for ‘if and only if’.
\mapsto	Maps-to arrow with a bar tail: x \mapsto x^2.
\longmapsto	Long version of \mapsto.
\hookrightarrow	Right arrow with a hook tail, for inclusions/embeddings.
\rightharpoonup	Right harpoon (half-arrow), used for weak convergence.
\rightleftharpoons	Paired opposing harpoons, as in chemical equilibrium.
\leadsto	Squiggly right arrow, ‘leads to’ (amssymb).
\uparrow, \downarrow	Upward and downward arrows.
\updownarrow	Double-headed vertical arrow.
\Uparrow, \Downarrow, \Updownarrow	Double-lined vertical arrows.
\nearrow, \searrow	Diagonal arrows northeast and southeast, e.g. increasing/decreasing to a limit.
\swarrow, \nwarrow	Diagonal arrows southwest and northwest.
\longrightarrow, \longleftarrow	Long single arrows.
\Longrightarrow, \Longleftarrow, \Longleftrightarrow	Long double arrows.
\xrightarrow{f}	Extensible right arrow with a label on top, growing to fit (amsmath).
\xleftarrow{f}	Extensible left arrow with a label on top (amsmath).

Math: big operators

Command	What it does
\sum_{i=1}^{n}	Summation sign with limits.
\prod_{i=1}^{n}	Product sign with limits.
\coprod	Coproduct (upside-down product) sign.
\int_0^1	Integral sign with bounds.
\iint	Double integral sign (amsmath).
\iiint	Triple integral sign (amsmath).
\oint	Contour (closed loop) integral sign.
\bigcap, \bigcup	Big intersection and union over a family of sets.
\bigsqcup	Big square-cup (disjoint union).
\bigvee, \bigwedge	Big OR and big AND over an index set.
\bigoplus, \bigotimes, \bigodot	Big circled plus, times, and dot for indexed sums and products of structures.
\biguplus	Big union-with-plus over an index set.
\limits	Forces the following operator’s sub/superscripts above and below: \int\limits_0^1.
\nolimits	Forces sub/superscripts to the side instead of above and below.

Math: delimiters and sizing

Command	What it does
\left( ... \right)	Auto-sized delimiter pair that grows to fit its contents.
\left. and \right.	Invisible partner when only one side of a sized pair is wanted, as in evaluation bars.
`\middle	`
\big( \Big( \bigg( \Bigg(	Manually sized delimiters, from slightly big to very big.
\bigl(...\bigr)	Sized delimiters with correct open/close spacing (also \Bigl, \biggl, \Biggl).
\lfloor, \rfloor	Floor brackets.
\lceil, \rceil	Ceiling brackets.
\langle, \rangle	Left and right angle bracket delimiters.
|	Double vertical bar delimiter (norm bars).
\lvert, \rvert	Absolute-value bars with correct delimiter spacing (amsmath).
\lVert, \rVert	Double bars for norms, with correct delimiter spacing (amsmath).
\backslash	Backslash as a math symbol or delimiter.

Math: accents and decorations

Command	What it does
\hat{x}	Small hat accent over one symbol.
\check{x}	Caron (inverted hat) accent.
\breve{x}	Breve (rounded) accent.
\acute{x}, \grave{x}	Acute and grave accents in math.
\tilde{x}	Tilde accent over one symbol.
\bar{x}	Short bar over one symbol.
\vec{v}	Small arrow over one symbol.
\dot{x}, \ddot{x}	One or two dots over a symbol, common for time derivatives.
\dddot{x}	Three dots over a symbol (amsmath).
\mathring{x}	Ring accent over a symbol.
\widehat{abc}	Wide hat that stretches over several symbols.
\widetilde{abc}	Wide tilde that stretches over several symbols.
\overrightarrow{AB}	Stretching right arrow over an expression, as in vectors from A to B.
\overleftarrow{AB}	Stretching left arrow over an expression.
\overline{x + y}	Line over a whole expression.
\underline{x + y}	Line under a whole expression (also works in text).
\overbrace{...}^{n}	Horizontal brace above an expression, with an optional label on top.
\underbrace{...}_{n}	Horizontal brace below an expression, with an optional label underneath.
\overset{!}{=}	Places a symbol above another, e.g. ‘must equal’ (amsmath).
\underset{i}{\max}	Places a symbol below another (amsmath).
\stackrel{\text{def}}{=}	Older kernel command stacking a symbol over a relation.
\boldsymbol{\beta}	Bold math that also bolds Greek letters and symbols (amsmath).
\prime	Prime symbol; x' is the usual shorthand for x^{\prime}.

Math: log-like operators

All typeset upright with correct spacing; the limit-taking ones put subscripts below in display math.

Command	What it does
\sin, \cos, \tan, \cot	The basic trigonometric functions.
\sec, \csc	Secant and cosecant.
\arcsin, \arccos, \arctan	Inverse trigonometric functions.
\sinh, \cosh, \tanh, \coth	Hyperbolic functions.
\exp, \ln, \log, \lg	Exponential and logarithms (\lg is log base 2 or 10 by convention).
\det, \dim, \ker, \deg	Determinant, dimension, kernel, degree.
\gcd, \hom, \arg, \Pr	Greatest common divisor, hom-sets, complex argument, probability.
\lim_{x \to 0}	Limit operator, upright with the subscript below in display math.
\limsup, \liminf	Limit superior and inferior.
\inf, \sup	Infimum and supremum operators, typeset upright.
\min, \max	Minimum and maximum operators, typeset upright with limits below in display math.
\bmod	Binary mod operator with operator spacing: a \bmod n.
\pmod{n}	Parenthesized trailing ‘(mod n)’.
\mod{n}	Trailing ‘mod n’ without parentheses (amsmath).
\operatorname{lcm}	One-off upright operator name without a preamble declaration (amsmath).
\operatorname*{ess\,sup}	One-off operator that takes limits below (amsmath).

Math: fractions, binomials, and stacking

Command	What it does
\frac{a}{b}	Stacked fraction: numerator over denominator.
\dfrac{a}{b}	Fraction forced to full display size, even inline (amsmath).
\tfrac{a}{b}	Fraction forced to small inline size, even in display math (amsmath).
\cfrac{a}{b}	Continued fraction with full-size nested levels (amsmath).
\sqrt{x}, \sqrt[3]{x}	Square root; the optional argument gives an nth root.
\binom{n}{k}	Binomial coefficient in parentheses (amsmath).
\dbinom{n}{k}, \tbinom{n}{k}	Display-size and text-size forced binomials (amsmath).
{n \choose k}	Plain TeX binomial primitive; discouraged in LaTeX, use \binom.
{a \over b}	Plain TeX fraction primitive; discouraged in LaTeX, use \frac.
{a \atop b}	Plain TeX stacking primitive without a bar; discouraged, use \substack or \genfrac.
\genfrac{(}{)}{0pt}{}{a}{b}	General fraction builder behind \frac, \binom, and friends (amsmath).
\substack{i < n \\ j < m}	Multi-line subscript under a big operator (amsmath).
\sideset{_a^b}{_c^d}{\prod}	Attaches indices to all four corners of a big operator (amsmath).
\prescript{a}{b}{X}	Left-hand super/subscripts, as in isotope notation (mathtools).

Math: spacing and styles

Command	What it does
\,	Thin math space, as between a number and its unit.
\:	Medium math space.
\;	Thick math space.
\!	Negative thin space, pulling symbols closer.
\quad, \qquad	One-em and two-em spaces, in math or text.
\displaystyle	Forces full display-math sizing, e.g. big limits inside inline math.
\textstyle	Forces inline-math sizing inside display math.
\scriptstyle, \scriptscriptstyle	Force subscript and sub-subscript sizing.

Math: letters, alphabets, and misc symbols

Command	What it does
\mathbb{R}	Blackboard bold letters for number sets (amssymb).
\mathbf{x}	Bold upright letters in math, common for vectors and matrices.
\mathcal{L}	Calligraphic capital letters, e.g. a loss or Lagrangian.
\mathfrak{g}	Fraktur letters, used in algebra and logic.
\mathscr{F}	Script capital letters, curlier than \mathcal (mathrsfs).
\mathrm{d}x	Upright (roman) letters in math, for units and multi-letter names.
\mathit{diff}	Italic multi-letter identifier with word-like spacing.
\mathsf{T}, \mathtt{x}	Sans-serif and typewriter letters in math.
\bm{\beta}	Bold math symbols, an alternative to \boldsymbol (bm package).
\text{if } x > 0	Normal upright text inside math with proper spacing (amsmath).
\infty	Infinity sign.
\partial	Partial derivative (curly d) sign.
\nabla	Nabla (del) operator for gradients and divergence.
\hbar	Reduced Planck constant, h with a bar.
\ell	Script lowercase l, used to avoid confusion with the digit 1.
\wp	Weierstrass p.
\Re, \Im	Real and imaginary part symbols (Fraktur R and I).
\aleph	Aleph, for infinite cardinals.
\emptyset	Empty set sign.
\varnothing	Rounder empty-set variant many authors prefer (amssymb).
\angle	Angle symbol.
\measuredangle	Measured-angle symbol with an arc (amssymb).
\triangle	Triangle symbol.
\square, \blacksquare	Open and filled squares; the filled one often ends proofs (amssymb).
\diamond, \lozenge	Small diamond operator; lozenge symbol (amssymb for the latter).
\top, \bot	Top (true) and bottom (false/undefined) symbols.
\forall, \exists	Universal (‘for all’) and existential (‘there exists’) quantifiers.
\nexists	Negated existential quantifier (amssymb).
\neg	Logical NOT sign.
\therefore, \because	Three-dot ‘therefore’ and ‘because’ signs (amssymb).
\flat, \natural, \sharp	Musical accidentals, also used in math notation.
\surd	Bare radical symbol without an argument.
\checkmark	Check mark (amssymb).
\cdots	Centered dots, between operators: x_1 + \cdots + x_n.
\vdots, \ddots	Vertical and diagonal dots, mostly in matrices.
\dotsb, \dotsc	Semantic dots: between binary operators, and between commas (amsmath).

amsmath and mathtools display tools

Command	What it does
\tag{...}	Replaces the automatic equation number with your own label (amsmath).
\tag*{...}	Like \tag but without the surrounding parentheses (amsmath).
\notag	Suppresses the equation number on one line of a numbered environment (amsmath).
\nonumber	Older synonym of \notag.
\numberwithin{equation}{section}	Numbers equations per section: (2.1), (2.2) (amsmath).
\intertext{...}	Interrupts an align block with a full-width line of text, keeping alignment (amsmath).
\shortintertext{...}	Like \intertext with less vertical space (mathtools).
\allowdisplaybreaks	Lets multi-line displays break across pages (amsmath).
\displaybreak	Requests a page break at this point of a display (amsmath).
\smashoperator{\sum_{i=1}^{n}}	Lets wide operator limits overhang so they do not push content apart (mathtools).
\mathclap{...}	Zero-width math content, for wide under/overscripts (mathtools).
\coloneqq	Colon-equals definition sign := with correct spacing (mathtools).
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}	Defines a delimiter macro with a starred auto-sizing form (mathtools).
\eqref{eq:loss}	Prints an equation number with its parentheses (amsmath).
\qedhere	Moves the end-of-proof square onto the current line, e.g. after a displayed equation (amsthm).

Math environments

Environment	What it does
equation	One displayed, numbered equation.
equation*	One displayed, unnumbered equation (amsmath).
align	Multiple displayed equations aligned at & marks, each numbered (amsmath).
align*	Aligned equations without numbers (amsmath).
gather	Multiple centered equations without alignment, each numbered (amsmath).
alignat	Aligned equations with manually controlled spacing between columns (amsmath).
flalign	Aligned equations pushed to the left and right margins (amsmath).
split	Splits one long equation across aligned lines under a single number, inside equation (amsmath).
multline	One long equation broken across lines: first line left, last line right (amsmath).
aligned, gathered	Building-block versions of align/gather usable inside another display (amsmath).
subequations	Numbers the equations inside as 1a, 1b, 1c (amsmath).
cases	Brace-grouped case distinctions, as in piecewise functions (amsmath).
dcases	cases with display-style entries so fractions stay full size (mathtools).
matrix	Bare matrix with no delimiters (amsmath).
pmatrix	Matrix wrapped in parentheses (amsmath).
bmatrix	Matrix wrapped in square brackets (amsmath).
Bmatrix	Matrix wrapped in curly braces (amsmath).
vmatrix	Matrix wrapped in vertical bars, standard determinant notation (amsmath).
Vmatrix	Matrix wrapped in double bars (amsmath).
smallmatrix	Compact matrix sized for inline use (amsmath).
array	Math-mode grid with per-column alignment, the math cousin of tabular.
eqnarray	Old three-column equation environment; discouraged, its spacing is wrong, use align.

Cross-referencing and links

Command	What it does
\label{fig:setup}	Names a spot (equation, figure, section) so you can refer to it.
\ref{fig:setup}	Prints the number of a labeled item.
\pageref{fig:setup}	Prints the page number where the label lives.
\cref{fig:setup}	Prints the number AND its type name automatically: ‘fig. 1’ (cleveref).
\Cref{fig:setup}	Capitalized \cref for the start of a sentence: ‘Figure 1’ (cleveref).
\crefrange{eq:a}{eq:d}	Prints a range: ‘eqs. 1 to 4’ (cleveref).
\labelcref{fig:setup}	Prints just the label number in cleveref style, without the type name (cleveref).
\vref{fig:setup}	Reference plus an automatic ‘on the next page’ phrase when needed (varioref).
\autoref{fig:setup}	hyperref’s typed reference: ‘Figure 1’, with the whole phrase linked.
\nameref{sec:intro}	Prints the title text of the referenced section (hyperref).
\href{https://example.com}{link text}	Makes a clickable link with custom text (hyperref).
\url{https://example.com}	Typesets a URL in typewriter type and makes it clickable.
\hyperref[sec:intro]{that section}	Makes arbitrary text link to a label (hyperref).
\hypertarget{spot}{...}	Creates a named link target anywhere in the document (hyperref).
\hyperlink{spot}{text}	Links to a \hypertarget (hyperref).
\phantomsection	Creates an anchor so links to unnumbered headings land in the right place (hyperref).
\texorpdfstring{$\alpha$}{alpha}	Gives a plain-text alternative for math in headings so PDF bookmarks stay valid (hyperref).
\pdfbookmark[1]{Title}{name}	Adds a manual PDF bookmark entry (hyperref).

Citations and bibliography

Command	What it does
\cite{knuth1984}	Cites a bibliography entry by key.
\nocite{key}	Adds an entry to the bibliography without citing it in the text; \nocite{*} adds everything.
\citep{knuth1984}	Parenthetical citation ‘(Knuth, 1984)’ in natbib author-year style.
\citet{knuth1984}	Textual citation ‘Knuth (1984)’ in natbib author-year style.
\citeauthor{knuth1984}	Prints just the author names (natbib and biblatex).
\citeyear{knuth1984}	Prints just the year (natbib and biblatex).
\citealp{knuth1984}	natbib parenthetical citation without the parentheses, for building your own.
\citealt{knuth1984}	natbib textual citation without parentheses around the year.
\parencite{knuth1984}	biblatex’s parenthetical citation, the analogue of \citep.
\textcite{knuth1984}	biblatex’s textual citation, the analogue of \citet.
\autocite{knuth1984}	biblatex citation that follows the style’s preferred form (parenthetical, footnote, etc.).
\footcite{knuth1984}	biblatex citation placed in a footnote.
\fullcite{knuth1984}	Prints the entry’s full bibliography text inline (biblatex).
\citetitle{knuth1984}	Prints the work’s title (biblatex).
\bibliography{refs}	BibTeX: prints the reference list from a .bib file.
\bibliographystyle{plainnat}	BibTeX: picks the reference format; classic styles include plain, unsrt, alpha, abbrv, ieeetr, acm, apalike.
\addbibresource{refs.bib}	biblatex: registers a .bib file in the preamble.
\printbibliography	biblatex: prints the reference list where you place it.
\bibitem{key}	One hand-written entry inside a thebibliography environment.
thebibliography (environment)	Hand-written reference list used when you skip BibTeX entirely.

Floats, figures, and tables

Command or environment	What it does
figure (environment)	Floating container for an image plus caption; LaTeX picks the final position.
figure* (environment)	Figure spanning both columns in a two-column document.
table (environment)	Floating container for a tabular plus caption; LaTeX picks the final position.
table* (environment)	Table spanning both columns in a two-column document.
\begin{figure}[htbp]	Placement hints: here, top, bottom, own page; ! relaxes rules, [H] (float package) means exactly here.
tabular (environment)	The actual grid of rows and columns: cells split by &, rows end with \\.
tabular* (environment)	Tabular stretched to a specified total width.
tabularx (environment)	Fixed-width table whose X columns share the leftover space (tabularx).
array (environment)	Math-mode grid with per-column alignment.
longtable (environment)	Table that can break across pages, with repeating headers (longtable).
minipage (environment)	Fixed-width mini page inside the page, used to place content side by side.
subfigure (environment)	One sub-panel with its own caption, like (a) and (b), inside a figure (subcaption).
wrapfigure (environment)	Figure with body text wrapping around it (wrapfig).
sidewaysfigure, sidewaystable (environments)	Floats rotated 90 degrees onto their own page (rotating).
landscape (environment)	Rotates whole pages to landscape, with the PDF page auto-rotated (pdflscape).
threeparttable (environment)	Wraps a table so footnotes align with the table width (threeparttable).
tablenotes (environment)	The notes list under a threeparttable, marked with \tnote{a}.
adjustbox (environment and \adjustbox)	Scales, resizes, or crops any content with key-value options (adjustbox).
\caption{...}	Adds a numbered caption to a figure or table; put \label after it.
\caption*{...}	Caption without a number or list entry (caption package).
\captionsetup{...}	Configures caption fonts, labels, and spacing (caption package).
\toprule	Heavy rule at the top of a booktabs table.
\midrule	Medium rule between a booktabs table’s header and body.
\bottomrule	Heavy rule at the bottom of a booktabs table.
\cmidrule(lr){2-3}	Partial rule spanning selected columns (booktabs).
\addlinespace	Small extra vertical space between booktabs rows, instead of a rule.
\hline	Full-width horizontal line in a plain tabular; booktabs rules usually look better.
\cline{2-3}	Horizontal line spanning selected columns in a plain tabular.
\vline	Vertical line at this point of a table row; column `
\multicolumn{2}{c}{Header}	Merges cells across columns in one row.
\multirow{2}{*}{Label}	Merges cells vertically across rows (multirow).
\arraystretch	Factor for table row height; set with \renewcommand{\arraystretch}{1.3}.
\tabcolsep	Length of the padding on each side of a tabular column.
\newcolumntype{C}{>{\centering\arraybackslash}X}	Defines a reusable column specifier (array package).
\endfirsthead	longtable: marks the end of the header shown on the first page only.
\endhead	longtable: marks the end of the header repeated on every following page.
\endfoot	longtable: marks the end of the footer shown at each page break.
\endlastfoot	longtable: marks the end of the footer shown only at the very end.
\FloatBarrier	Stops floats drifting past this point (placeins).

Footnotes

Command	What it does
\footnote{...}	Puts a note at the bottom of the page, marked with an automatic number.
\footnotemark	Prints just the footnote marker, for places where \footnote is not allowed.
\footnotetext{...}	Supplies the text for an earlier \footnotemark.

Theorems and proofs

Command or environment	What it does
\newtheorem{lemma}{Lemma}	Declares a theorem-like environment (amsthm).
\newtheorem*{remark}{Remark}	Declares an unnumbered theorem-like environment (amsthm).
\theoremstyle{definition}	Sets the look (plain, definition, remark) for following \newtheorem declarations (amsthm).
theorem (environment)	Numbered theorem block, created by \newtheorem{theorem}{Theorem}.
proof (environment)	Proof block that prints ‘Proof.’ and ends with the QED square (amsthm).

Verbatim, code, and listings

Command or environment	What it does
`\verb	code
verbatim (environment)	Block of text printed exactly as typed, in typewriter font.
\verbatiminput{file.txt}	Prints a whole file verbatim (verbatim package).
lstlisting (environment)	Source code listing with optional syntax highlighting (listings).
`\lstinline	code
\lstset{language=Python}	Configures listings defaults: language, numbering, colors (listings).
\lstinputlisting{script.py}	Typesets a whole source file as a listing (listings).
minted (environment)	Pygments-powered highlighted code blocks; needs -shell-escape at compile time (minted).
`\mintinline{python}	code

Beamer (slides)

Command or environment	What it does
frame (environment)	One Beamer slide: \begin{frame}{Slide title} ... \end{frame}.
\frame{...}	Beamer’s one-command slide form; the frame environment is the usual way.
\frametitle{...}	Sets the slide title from inside a frame.
\framesubtitle{...}	Sets a smaller subtitle under the frame title.
\titlepage	Beamer: inside a frame, prints the title slide from your title metadata.
\tableofcontents[currentsection]	Outline slide highlighting the section you are in.
\pause	Beamer: reveals the rest of the frame on the next slide step.
\onslide<2->	Content appears from a given overlay step onward.
\only<2>{...}	Content exists only on the given steps and takes no space elsewhere.
\uncover<2->{...}	Content is invisible before its step but always reserves its space.
\visible<2->{...}, \invisible<2>{...}	Show or hide content on given steps without changing layout.
\alert{...}	Highlights text in the theme’s alert color, usually red.
block (environment)	Titled box in the theme’s standard color.
alertblock (environment)	Titled box in the alert color, for warnings or key points.
exampleblock (environment)	Titled box in the example color, usually green.
columns (environment) and \column{0.5\textwidth}	Side-by-side layout regions on a slide.
\usetheme{Madrid}	Beamer: picks the presentation theme in the preamble.
\usecolortheme{seahorse}	Swaps only the color palette of the theme.
\usefonttheme{serif}	Swaps only the font choices of the theme.
\setbeamertemplate{navigation symbols}{}	Overrides one theme element, here removing the navigation icons.
\setbeamercolor{title}{fg=black}	Overrides one theme color.
\note{...}	Speaker notes attached to a frame, shown only in notes output.

TikZ and diagrams

Command or environment	What it does
tikzpicture (environment)	Canvas for TikZ drawings; all \draw and \node commands go inside it.
\tikz	One-shot inline picture: \tikz \draw (0,0) circle (2pt);.
\draw (0,0) -- (1,1);	TikZ path command that draws lines and shapes; options like [thick, red, ->] style it.
\fill	TikZ path command that fills a shape instead of stroking it.
\filldraw	TikZ path command that both fills and outlines a shape.
\shade	TikZ path command that fills with a gradient.
\clip	TikZ path that restricts all later drawing to its interior.
\path	TikZ path that computes coordinates without drawing, e.g. for placing nodes.
\node at (0,0) {label};	TikZ command that places text or shapes at coordinates.
\coordinate (a) at (1,2);	Names a point for reuse in later paths.
\foreach \i in {1,...,5}	Loop that repeats drawing code over a list (TikZ/pgffor).
\tikzset{mystyle/.style={...}}	Defines reusable TikZ styles the modern way.
\tikzstyle	Old style-definition syntax; deprecated, use \tikzset.
\usetikzlibrary{positioning}	Loads extra TikZ features in the preamble.
\matrix (TikZ)	Grid-aligned arrangement of nodes inside a tikzpicture.
tikzcd (environment)	Grid for commutative diagrams; cells split by & (tikz-cd).
\arrow[r, "f"]	Draws an arrow between cells in a tikz-cd commutative diagram.

Units (siunitx)

Command	What it does
\num{12345.678}	Formats a number with proper digit grouping and decimal markers.
\qty{9.8}{\metre\per\second\squared}	Number with unit, correctly spaced (siunitx v3 name).
\unit{\kilo\gram}	Unit alone (siunitx v3 name).
\SI{9.8}{\metre\per\second\squared}	v2 name of \qty; still widely seen in papers.
\si{\kilo\gram}	v2 name of \unit.
\sisetup{...}	Global siunitx configuration.
\DeclareSIUnit{\parsec}{pc}	Defines a custom unit (siunitx).

Glossaries and acronyms

Command	What it does
\gls{svm}	Prints a glossary or acronym entry, expanding it on first use (glossaries).
\Gls{svm}	Capitalized form for sentence starts (glossaries).
\glspl{svm}	Plural form of the entry (glossaries).
\newglossaryentry{tree}{name=tree, description={...}}	Declares a glossary term (glossaries).
\newacronym{svm}{SVM}{support vector machine}	Declares an acronym with short and long forms (glossaries).
\acrshort{svm}, \acrlong{svm}	Force the short or long form regardless of first use (glossaries).
\makeglossaries	Preamble command that activates glossary/acronym processing (glossaries).
\printglossary	Prints one glossary list where you place it (glossaries).
\printglossaries	Prints the glossary and acronym lists where you place it (glossaries).

Algorithms and pseudocode

Keyword commands are from algpseudocode (algorithmicx); the algorithm float wraps them.

Command or environment	What it does
algorithm (environment)	Floating container for pseudocode, with a caption and number (algorithm).
algorithmic (environment)	The pseudocode body itself, holding the keyword commands (algpseudocode).
\State	One statement line of pseudocode.
\If{...}, \ElsIf{...}, \Else, \EndIf	Conditional block keywords.
\For{...}, \ForAll{...}, \EndFor	Loop keywords over a range or a set.
\While{...}, \EndWhile	While-loop keywords.
\Function{Name}{args}, \EndFunction	Function definition block.
\Procedure{Name}{args}, \EndProcedure	Procedure definition block.
\Return	The return keyword.
\Comment{...}	Right-aligned comment on a pseudocode line.
\Require, \Ensure	Preconditions and postconditions lines at the top of an algorithm.

Language, quoting, and editorial packages

Command	What it does
\selectlanguage{german}	Switches the active language: hyphenation, captions, dates (babel).
\foreignlanguage{french}{...}	Typesets a short passage under another language’s rules (babel).
\enquote{...}	Context-aware quotation marks that nest and localize correctly (csquotes).
\todo{Fix this}	Margin note flagging work to do (todonotes).
\listoftodos	Prints a list of all todo notes (todonotes).
\missingfigure{...}	Placeholder box for a figure you have not made yet (todonotes).
\xspace	At the end of a macro, adds a space unless punctuation follows (xspace).
\patchcmd{\cmd}{find}{replace}{ok}{fail}	Patches an existing macro’s definition in place (etoolbox).
\apptocmd, \pretocmd	Append or prepend code to an existing macro (etoolbox).
\newtoggle{draft}, \toggletrue{draft}, \iftoggle{draft}{...}{...}	Lightweight boolean flags (etoolbox).

Layout and typography packages in one line

Package or command	What it does
\setstretch{1.25}	Sets an exact line-spacing factor (setspace).
\doublespacing	Switches to double line spacing (setspace).
\onehalfspacing	Switches to one-and-a-half line spacing (setspace).
\singlespacing	Switches back to single line spacing (setspace).
spacing (environment)	Sets a custom line-spacing factor for its contents (setspace).
\titleformat{\section}{...}{...}{...}{...}	Redesigns how a sectioning heading looks (titlesec).
\titlespacing{\section}{0pt}{12pt}{6pt}	Adjusts the space around a heading (titlesec).
\setlist[itemize]{noitemsep}	Configures list spacing and labels globally or per level (enumitem).
parskip (package)	Switches the document to block paragraphs: space between, no indent.
microtype (package)	Subtle protrusion and expansion that improves justification; just load it.
multicols (environment)	Balanced multi-column text without the twocolumn class option (multicol).

Chemistry, physics, and domain notation

Command	What it does
\ce{H2O}	Typesets a chemical formula or reaction (mhchem).
\chemfig{...}	Draws a chemical structure diagram (chemfig).
`\braket{\phi	\psi}`

Publisher class commands

Command or environment	What it does
\IEEEauthorblockN{...}	IEEEtran: formats an author name block in the IEEE conference title area.
\IEEEauthorblockA{...}	IEEEtran: formats an author affiliation block in the IEEE conference title area.
\ccsdesc[500]{...}	acmart: declares one ACM CCS concept for the paper’s classification.
CCSXML (environment)	acmart: holds the machine-readable ACM CCS concepts XML from the ACM classification tool.
\University{...}	Class-specific metadata command seen in thesis templates, not standard LaTeX.

Environments in general

An environment is a region opened with \begin{name} and closed with \end{name}; everything between the two gets that environment’s behavior. The full story is in commands vs environments. The general-purpose ones:

Environment	What it does
document	The body of every document lives between \begin{document} and \end{document}.
abstract	Prints the paper’s abstract with the class’s standard heading and layout.
titlepage	Wraps a hand-made full title page; the page is unnumbered.
center	Centers its contents horizontally.
flushleft	Left-aligns its contents, ragged right.
flushright	Right-aligns its contents, ragged left.
itemize	Bulleted list; each entry starts with \item.
enumerate	Numbered list; each entry starts with \item.
description	Labeled list; entries start with \item[Label].
\item	Starts one entry inside itemize, enumerate, or description lists.
quote	Indented block for short quotations, no paragraph indent.
quotation	Indented block for longer quotations, with paragraph indents.
verse	Indented block for poetry, where \\ ends each verse line.
sloppypar	Paragraphs typeset with relaxed line-breaking, the environment form of \sloppy.
list	The general list builder that itemize and friends are defined from.
trivlist	Bare-bones list with no labels or margins, used inside macro definitions.
filecontents	Writes its body out to a file at compile time, e.g. to ship a .bib inside the .tex.
appendices	Wraps the appendix chapters, enabling \appendixpage and per-appendix tools (appendix package).

Where to go next

This page is the dictionary; the lessons are the grammar. For a paste-ready one-pager, keep the cheatsheet open. For the difference between \command{...} and \begin{...} blocks, read commands vs environments. And for finding a symbol you can picture but cannot name, use math symbols. To see what any math-mode command looks like, paste it into the live preview and watch it render.