This book develops a new approach to the modular representation theory of finite groups, introducing the reader to an active area of research in pure mathematics. It gives a comprehensive treatment of the theory of G-algebras and shows how it can be used to solve a number of problems about blocks, modules and almost-split sequences. The text gives easy access to some complex recent results, and provides a clear exposition of the important but difficult work in Puig's theory. This book will be of greatest interest to postgraduate students in algebra.