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Which one should I use: \begin{align} or \begin{aligned}?

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You use align outside the math mode, and aligned inside the math mode. – kennytm Jan 12 '11 at 9:16
@KennyTM: Only that? – xport Jan 12 '11 at 9:17
I don't study amsmath in detail, but that's the only difference I perceive. I could be wrong though :) – kennytm Jan 12 '11 at 9:19
…: Answers can be found in the »amsmath« manual or in the »Math mode« document. – Thorsten Donig Jan 12 '11 at 9:20
@Thorsten + @KennyTM : Thanks. – xport Jan 12 '11 at 9:22

If you have a series of equations that you want to have mutual alignment, then you would use align. If the equations are part of a larger equation, then aligned is the right environment.

I often will use \begin{equation}\begin{aligned} ... \end{aligned}\end{equation} to give a single equation number to a group, for example if I'm showing steps.

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align is used for entering to math-mode while aligned is used for multiple horizon alignment. For example

    2x+3 &= 7 & 2x+3-3 &= 7-3 \\
    2x &= 4 & \frac{2x}2 &= \frac42\\
    x &= 2

ps. the example is adapted from Math Mode document of Herbert Voß.

For grouping the multiple lines equation, you should use gather or multline.

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You can use align inside subequation to get the numbering (1a) and (1b). Then you can refer the the equation system with (1) and to the subequations directly.

a &= b \\  
c &= d  
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