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I 'm currently reading topics relating to type IIB superstring theory. One of the things I am always confused with is Groups. I looked on various websites including Wikipedia but I still haven't quite got it. Could anyone please give me a nice introduction about Groups?

What are GL(n), SL(n), O(n), SO(n), U(n), SU(n), Sp(n) ?? I know what they 're called, but I don't understand their operations and significance.

For example:

What are the differences between SO(24) and SO(25)?

What are the differences between SO(3) and SO (2, 1)?

Why is the two sphere S^{2} = SO(3) / SO(2)?

Why is the Anti-de Sitter space AdS^{2} = SO(2, 1) / SO(1, 1)?

Many thanks!

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# Group Theory

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