Taking up the works of Harish-Chandra, Langlands, Borel, Casselman, Bernstein and Zelevinsky, among others, on the complex representation theory of a p -adic reductive group G, the author explores the representations of G over an algebraic closure Fl of a finite field Fl with l1 p elements, which are called 'modular representations'. The main feature of the book is to develop the theory of types over Fl, and to use this theory to prove fundamental results in the theory of modular representations.

"The present book is of evident importance to everyone interested in the representation...