The first systematic exposition of the theory of derived categories, with key applications in commutative and noncommutative algebra.

Amnon Yekutieli is Professor of Mathematics at Ben-Gurion University of the Negev, Israel. His research interests are in algebraic geometry, ring theory, derived categories and deformation quantization. He has taught several graduate-level courses on derived categories and has published three previous books.

Introduction; 1. Basic facts on categories; 2. Abelian categories and additive functors; 3. Differential graded algebra; 4. Translations and standard triangles; 5. Triangulated categories and functors; 6. Localization of categories; 7. The derived category D(A,M); 8. Derived functors; 9. DG and triangulated bifunctors; 10. Resolving subcategories of K(A,M); 11. Existence of resolutions; 12. Adjunctions, equivalences and cohomological dimension; 13. Dualizing complexes over commutative rings; 14. Perfect and tilting DG modules over NC DG rings; 15. Algebraically graded noncommutative rings; 16. Derived torsion over NC graded rings; 17. Balanced dualizing complexes over NC graded rings; 18. Rigid noncommutative dualizing complexes; References; Index.