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\documentclass[a4paper]{book}
\usepackage{amsmath}
\begin{document}
Plain aligns
\begin{align}
A =& B \\
C =& D \\
\end{align}
\begin{align}
A =& B \\
C =& D \\
&+E \notag
\end{align}
Equations \eqref{eq:before} and \eqref{eq:after}:
\begin{align}
\label{eq:before}
&x \quad c_1,
\end{align}
and
\begin{align}
&y \quad c_2,
\label{eq:after}
\end{align}
Aligned within math
\[\begin{aligned}
A =& B
\end{aligned}
\]
Tendency to see the ampersand before aligned has started
\[
C =\left\{\begin{aligned}
& D \end{aligned}\right.
\]
Align with aligned
\begin{align*}
A & B\\
C &\left\{\begin{aligned}
& D \end{aligned}\right.
\end{align*}
\begin{align}
A =& \left\{
\begin{aligned}
B & \text{if}\\
C & \text{otherwise}
\end{aligned}\right.
\end{align}
Or even
\begin{align}
\begin{aligned}
& a\\
& b
\end{aligned}
\end{align}
Equation with split; Ampersand before relation
\begin{equation}
\begin{split}
C &= D \\
&{}+E
\end{split}
\end{equation}
or after
\begin{equation}
\begin{split}
C =& D \\
&{}+E
\end{split}
\end{equation}
Gather with split
\begin{gather}
A = B \\
\begin{split}
C &= D \\
&{}+E
\end{split}\\
F = G
\end{gather}
Align with split.
Notice that the split acts like a column pair in the align.
\begin{align}
A &= B \\
\begin{split}
C &= D \\
&{}+E
\end{split}\\
F &= G\\
H &= I
\end{align}
\begin{align}
A =&\ B \\
B=& - C \\
\begin{split}
C =& -D + E + F + G + H\\
&+I
\end{split}
\end{align}
2-Column align, with missing columns
\begin{align}
A &= B &
C &= D \\
E &= F \\
H &= I &
J &= K
\end{align}
2-Column align with split;
Note that you should omit double slash from last line of split!
\begin{align}
A &= B &
C &= D \\
\begin{split}
E &= F \\
&{} + G
\end{split}\\
H &= I &
J &= K
\end{align}
\begin{align}
A &= B &
C &= D \\
X &= Y &
\begin{split}
E &= F \\
&{} + G
\end{split}\\
H &= I & J &= K \\
\begin{split}
L &= M\\
&{}+N
\end{split} &
O &= P\\
Q &= R &
S &= T
\end{align}
Multiple splits in multicolumn align.
Note how each split block contributes to a single row, but it is
horizontally aligned as if it were a column pair in the align.
\begin{align}
A &= B+b+c+d &
C &= D \\
\begin{split}
E+e+f+g &= F \\
&{} + G
\end{split} &
\begin{split}
L &= M\\
&{}+N \\
&{}+Z
\end{split} \\
Q &= R &
S &= T
\end{align}
%\end{document}
%\end{document}
\end{document}
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