BOOK REVIEWS REPRESENTATIONS AND COHOMOLOGY I: Basic representation theory of finite groups and associative algebras

Cohomology of finite groups developed rapidly during the seventies and eighties and is maturing into an important branch of algebra of interest in its own right, having applications in algebra, to group theory and representation theory, and in topology, especially to homotopy theory. Both Benson and Evens are at the forefront of the research, and their books are valuable contributions to the literature. Evens' book is beautifully written and provides a fine introduction to cohomology of groups, finite or infinite, which is especially suited to the algebraist. Evens is strongly influenced by his interest in finite groups, and the last three chapters are directed towards the cohomology theory of finite groups. Benson takes a very different approach, covering a great deal of ground from representation theory through to homotopy theory. Benson's enthusiasm comes across in his writing. The volumes begin with very basic material and progress to an advanced level across a very broad range of mathematics. There is again an emphasis on finite groups.