1. Chain complexes; 2. Derived functors; 3. Tor and Ext; 4. Homological dimensions; 5. Spectral sequences; 6. Group homology and cohomology; 7. Lie algebra homology and cohomology; 8. Simplicial methods in homological algebra; 9. Hothschild and cyclic homology; 10. The derived category; Appendix: category theory language.

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A portrait of the subject of homological algebra as it exists today.

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"It is...the ideal text for the working mathematician need- ing a detailed description of the fundamentals of the subject as it exists and is used today; the author has succeeded brilliantly in his avowed intention to break down 'the technological barriers between casual users and experts'." Kenneth A. Brown, Mathematical Reviews "By collecting, organizing, and presenting both the old and the new in homological algebra, Weibel has performed a valuable service. He has written a book that I am happy to have in my library." Joseph Rotman, Bulletin of the American Mathematical Society

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