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I'm interested in finding a textbook to learn group cohomology, a book that contains a lot of examples and also a lot of good exercises to test my understanding. I would appreciate some feedback. Thanks.


Added from the comments:

I like group extensions and finite Galois groups. These days, I'm mostly interested in doing a lot of hand computations in group cohomology, playing around, finding and creating examples when I'm inspired to created some.

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    $\begingroup$ One canonical reference is K. Brown's cohomology of groups, especially suitable if you have a geometric and topological flair. It has lots of good exercises, ranging from very simple to quite involved. Any introduction to homological algebra contains at least a section on group cohomology. Here, I'd especially recommend Hilton-Stammbach's classic. $\endgroup$ – t.b. May 26 '11 at 23:01
  • $\begingroup$ I like group extensions and finite Galois groups. These days, I'm mostly interested in doing a lot of hand computations in group cohomology, playing around, finding and creating examples when I'm inspired to created some. Learning by doing. $\endgroup$ – Iota May 26 '11 at 23:33
  • $\begingroup$ I second Brown's cohomology of groups. $\endgroup$ – Josh May 26 '11 at 23:40
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Ken Brown's textbook Cohomology of Groups is clearly the first to start with, and the ultimate guide... you may find somewhere on the internet my solutions manual for that text (I studied under him for a while).

The next step is Alejandro Adem's textbook Cohomology of Finite Groups (focuses on computations).
Then Leonard Evens' textbook The Cohomology of Groups (focuses on his Norm-map construction).

Going the route of Galois Theory, you're lead to J.P. Serre's textbook Galois Cohomology.

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    $\begingroup$ @Gerig I cant find your solutions manual on the internet. It definitely would be useful for self study. $\endgroup$ – messi Apr 2 '13 at 8:55

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