Multi-line equations that line up

A derivation of several steps looks best with the equals signs stacked in one column, so the eye can track what changed from line to line. The amsmath package provides the align environment for exactly this, plus a small family of relatives for the cases where alignment is not what you want.

\usepackage{amsmath}
\begin{align}
 a &= b + c \\
 d &= e + f + g
\end{align}

How align reads

Each line is one equation, ended by \\; the last line needs none. The & marks the alignment point, and every line’s & lands in the same column. Placing & immediately before the equals sign is the standard habit, so the equals signs stack and the left-hand sides hang off to the left. Every line receives its own equation number; write align* to number none, or add \notag to individual lines to skip just those, as shown in numbers and pointers for equations.

The environment opens display math by itself, so it must not sit inside \[ ... \] or $ ... $; nesting it in another math environment produces confusing errors.

The family

gather handles several equations with no shared alignment point; it centers each line and numbers each one. split builds one multi-line equation under a single number and must sit inside equation. multline breaks one overlong formula without alignment, first line flush left and last flush right. The last two are treated in detail in equations that will not fit.

Choosing comes down to two distinctions: whether the lines are separate equations or one broken equation, and whether there is an alignment point worth stacking. Separate and aligned calls for align, separate and centered for gather, single and aligned for split, single and unaligned for multline.

Common mistakes

A line without & still compiles, but it centers independently and nothing lines up. Two & on a line start a second column pair, which align reads as a second column of equations set side by side; if your output has equations marching to the right, count your ampersands. A trailing \\ on the final line adds an empty row, which appears as odd vertical space below the block. Type a three-step derivation in the live playground to watch the alignment come together.