Eminent mathematicians have presented papers on homological and combinatorial techniques in group theory. The lectures are aimed at presenting in a unified way new developments in the area.

This book is about the interplay between algebraic topology and the theory of infinite discrete groups. It is a hugely important contribution to the field of topological and geometric group theory, and is bound to become a standard reference in the field. To keep the length reasonable and the focus clear, the author assumes the reader knows or can easily learn the necessary algebra, but wants to see the topology done in detail. The central subject of the book is the theory of ends. Here the author adopts a new algebraic approach which is geometric in spirit.

This introduction to some basic ideas in algebraic topology is devoted to the foundations and applications of homology theory. After the essentials of singular homology and some important applications are given, successive topics covered include attaching spaces, finite CW complexes, cohomology products, manifolds, Poincare duality, and fixed point theory. This second edition includes a chapter on covering spaces and many new exercises.

Aimed at second year graduate students, this text introduces them to cohomology theory (involving a rich interplay between algebra and topology) with a minimum of prerequisites. No homological algebra is assumed beyond what is normally learned in a first course in algebraic topology, and the basics of the subject, as well as exercises, are given prior to discussion of more specialized topics.

Homological algebra, because of its fundamental nature, is relevant to many branches of pure mathematics, including number theory, geometry, group theory and ring theory. Professor Northcott's aim is to introduce homological ideas and methods and to show some of the results which can be achieved. The early chapters provide the results needed to establish the theory of derived functors and to introduce torsion and extension functors. The new concepts are then applied to the theory of global dimensions, in an elucidation of the structure of commutative Noetherian rings of finite global dimension and in an account of the homology and cohomology theories of monoids and groups. A final section is devoted to comments on the various chapters, supplementary notes and suggestions for further reading. This book is designed with the needs and problems of the beginner in mind, providing a helpful and lucid account for those about to begin research, but will also be a useful work of reference for specialists. It can also be used as a textbook for an advanced course.

The landscape of homological algebra has evolved over the last half-century into a fundamental tool for the working mathematician. This book provides a unified account of homological algebra as it exists today. The historical connection with topology, regular local rings, and semi-simple Lie algebras are also described. This book is suitable for second or third year graduate students. The first half of the book takes as its subject the canonical topics in homological algebra: derived functors, Tor and Ext, projective dimensions and spectral sequences. Homology of group and Lie algebras illustrate these topics. Intermingled are less canonical topics, such as the derived inverse limit functor lim1, local cohomology, Galois cohomology, and affine Lie algebras. The last part of the book covers less traditional topics that are a vital part of the modern homological toolkit: simplicial methods, Hochschild and cyclic homology, derived categories and total derived functors. By making these tools more accessible, the book helps to break down the technological barrier between experts and casual users of homological algebra.