Henning Krause is a Professor of Mathematics at the University of Paderborn Dieter Happel is a Professor of Algebra in the Fakultat fur Mathematik at theTechnische Universitat Chemnitz Lidia Angeleri Hugel is a Professor at the Universita degli Studi dell'Insubria

'… presents a key and very active part of contemporary representation theory in a concise but complete way. It will be indispensible for a wide audience, from graduate students to active researchers in algebra, geometry and topology.' European Mathematical Society Newsletter

• 1. Introduction; 2. Basic results of classic tilting theory L. Angeleri Hügel, D. Happel and H. Krause; 3. Classification of representation-finite algebras and their modules T. Brüstle; 4. A spectral sequence analysis of classical tilting functors S. Brenner and M. C. R. Butler; 5. Derived categories and tilting B. Keller; 6. Fourier-Mukai transforms L. Hille and M. Van den Bergh; 7. Tilting theory and homologically finite subcategories with applications to quasihereditary algebras I. Reiten; 8. Tilting modules for algebraic groups and finite dimensional algebras S. Donkin; 9. Combinatorial aspects of the set of tilting modules L. Unger; 10. Cotilting dualities R. Colpi and K. R. Fuller; 11. Infinite dimensional tilting modules and cotorsion pairs J. Trlifaj; 12. Infinite dimensional tilting modules over finite dimensional algebras Ø. Solberg; 13. Representations of finite groups and tilting J. Chuang and J. Rickard; 14. Morita theory in stable homotopy theory B. Shipley.