At the crossroads of representation theory, algebraic geometry and finite group theory, this book blends together many of the main concerns of modern algebra, synthesising the past 25 years of research, with full proofs of some of the most remarkable achievements in the area. Cabanes and Enguehard follow three main themes: first, applications of etale cohomology, leading to the proof of the recent Bonnafe-Rouquier theorems. The second is a straightforward and simplified account of the Dipper-James theorems relating irreducible characters and modular representations. The final theme is local representation theory. One of the main results here is the authors' version of Fong-Srinivasan theorems. Throughout the text is illustrated by many examples and background is provided by several introductory chapters on basic results and appendices on algebraic geometry and derived categories. The result is an essential introduction for graduate students and reference for all algebraists.