The align environment is provided by packages such as amsmath and mathtools. The alignment reference point is indicated by &, which should be placed just before the sign of relation or operation in order to obtain proper spacing. The end of all lines except the last is indicated by \\. The related environment alignat allows horizontal space between equations on the same line to be explicitly specified. Both align and alignat produce equation numbers on each line; numbers can be omitted from individual lines with \notag or \nonumber. Starred versions without numbering are provided as well.
The sub-environments aligned and alignedat are building blocks to be used when the aligned component is only part of a longer multi-line structure. The width of each component is only as large as necessary, so that it can, for example, be set within delimiters.
Use of these environments is described in the amsmath users guide, which on a TeX Live system can be accessed by texdoc amsmath.