This book is an introduction to the contemporary representation theory of Artin algebras, by three very distinguished practitioners in the field. Beyond assuming some first-year graduate algebra and basic homological algebra, the presentation is entirely self-contained, so the book is a suitable introduction for any mathematician (especially graduate students) to this field. The main aim of the book is to illustrate how the theory of almost split sequences is used in the representation theory of Artin algebras. However, other foundational aspects of the subject are developed. These results give concrete illustrations of some of the more abstract concepts and theorems. The book includes complete proofs of all theorems, and numerous exercises.

‘This book will be the major source for students studying in this field, and a reference for the material it covers.’

Peter Webb Source: Bulletin of the London Mathematical Society

‘A very good source of information for people entering the field.’

L. Marki Source: International Mathematical News

‘... written in a clear comprehensive style with full proofs. It can very well serve as an excellent reference as well as a textbook for graduate students.’

Source: EMS Newletter