This is the second of two volumes which have grown out of about seven years of graduate courses on various aspects of representation theory and cohomology of groups, given at Yale, Northwestern and Oxford. In this second volume, we concentrate on cohomology of groups and modules. We try to develop everything from both an algebraic and a topological viewpoint, and demonstrate the connection between the two approaches. Having in mind the die-hard algebraist who refuses to have anything to do with topology, we have tried to make sure that if the reader omits all sections involving topology, the rest is still a coherent treatment of the subject. But by trying to present the topology with as few prerequisites as possible, we hope to entice such a reader to a more broad-minded point of view. Thus Chapter 1 consists of a predigested summary of the topology required to understand what is happening in Chapter 2.

In Chapter 2, we give an overview of the algebraic topology and K-theory associated with cohomology of groups, and especially the extraordinary work of Quillen which has led to his definition of the higher algebraic K-groups of a ring.

The algebraic side of the cohomology of groups mirrors the topology, and we have always tried to give algebraic proofs of algebraic theorems. For example, in Chapter 3 you will find B. Venkov's topological proof of the finite generation of the cohomology ring of a finite group, while in Chapter 4 you will find L. Evens' algebraic proof.