I would like to know more about group cohomology. I know that there are chapters about group cohomology in some group theory textbooks, for example in Rotman's. However my PhD asvisor told me that he did not really like the way in which it was presented, but could not give my any other reference. I was also wondering if there is some text completely devoted to an introduction to group cohomology...
Mentioned early Brown's Cohomology of groups is probably best as introductory reference
There are some books which I like and are not widely known.
Adem, Milgram, Cohomology of finite groups — contains rarely mentioned in most basic group theory textbooks Quillen-Venkov and Kan-Thurston theorems, and applications in number theory (Brauer grous etc.)
Karpilovsky, Group representations, p. 2 — half of book is devoted to detailed analysis of second cohomology group and its properties
Stammbach, Homology in Group Theory — here extensions with abelian kernel within a given group variety are discussed
Gruenberg, Cohomological Topics in Group Theory and
Gruenberg, Categories of group extensions — in some sense, more accessible (and extended) versions of previous text
Ю. Кузьмин, Гомологическая теория групп — unfortunately no English translation exists, but you can look at formulas in ch. 4 §8 and ch. 5 §7 or try it with translator (mathematical texts are not very hard to translate usually)