These two volumes 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. The pace is brisk, and beginning graduate students would certainly be advised to have at hand a standard algebra text, such as for example Jacobson.

The chapters are not organised for sequential reading. Chapters 1, 2, 3 of Volume I and Chapter 1 of Volume II should be treated as background reference material, to be read sectionwise (if there is such a word). Each remaining chapter forms an exposition of a topic, and should be read chapterwise (or not at all).

The centrepiece of the first volume is Chapter 4, which gives a not entirely painless introduction to Auslander-Reiten type representation theory. This has recently played an important rôle in representation theory of finite groups, especially because of the pioneering work of K. Erdmann– and P. Webb. Our exposition of blocks with cyclic defect group in Chapter 6 of Volume I is based on the discussion of almost split sequences in Chapter 4, and gives a good illustration of how modern representation theory can be used to clean up the proofs of older theorems.

While the first volume concentrates on representation theory with a cohomological flavour, the second concentrates on cohomology of groups, while never straying very far from the pleasant shores of representation theory. In Chapter 2 of Volume II, 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.