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I studied algebra and group theory at the university about 20 years ago. Lately I've been reading the occasional maths book/article and they mention things like $\rm{SO}(n)$ and $\rm{SU}(2)$ as classes of groups.

I can see each of these are different categories of groups and remember studying these individually, however it seems these categories mean more now and are a part of some larger theory.

If this is the case, if someone could point me towards a reference / book (kindle would be good) it would be appreciated.

tia

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    I suggest that you read the [Wikipedia page on Lie groups](http://en.wikipedia.org/wiki/Lie_group) and have a look at the references given there. Your examples $\operatorname{SU}(n)$ and $\operatorname{SO}(n)$ are *compact Lie groups*. Personally, I found the notes by [Hilgert and Neeb](http://math-www.upb.de/user/hilgert/static/Lehrveranstaltungen/lgla.pdf) quite good (link goes to a pdf on Hilgert's homepage), but they may be a bit advanced.2011-05-07
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    @t.b. The link is broken, teebee. :(2012-08-05
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    @FortuonPaendrag: yes, these notes were published as a *Springer Monograph in Mathematics* and subsequently removed from the homepage. Google books link: Hilbert, Neeb, *[Structure and Geometry of Lie groups](http://books.google.com/books?id=PYWoqskGw1YC)*.2012-08-05
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    HilGert :) ${}{}$2012-08-05

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What you're looking for is the theory of Lie groups. There are many books about this at different levels of sophistication. Perhaps a good place to begin is Stillwell's book Naive Lie Theory.

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    Many thanks, I've been meaning to read about these as well :-)2011-05-07