A self-contained introduction is given to J. Rickard's Morita theory for derived module categories and its recent applications in representation theory of finite groups. In particular, Brou¿ conjecture is discussed, giving a structural explanation for relations between the p-modular character table of a finite group and that of its "p-local structure". The book is addressed to researchers or graduate students and can serve as material for a seminar. It surveys the current state of the field, and it also provides a "user's guide" to derived equivalences and tilting complexes. Results and proofs are presented in the generality needed for group theoretic applications. TOC:Introduction.- Basic definitions and examples.- Rickard's fundamental theorem.- Some modular and local representation theory.- One-sided tilting complexes for group rings.- Tilting with additional structure : Two-sided tilting complexes.- Historical remarks.- Bernhard Keller: On the construction of triangle equivalences.- Jeremy Rickard: Triangulated categories in the modular representation theory of finite groups.- Raphael Rouquier: The derived category of blocks with cyclic defect groups.- Markus Linckelmann: On stable equivalences of Morita type.
