One, Preparatory -- 0. Algebras, Modules, Complexes -- I. Cohomology Groups and Problems Giving Rise to Them -- II. Tensor Product -- Two, Basic -- III. Homological Concepts (General Properties) -- IV. Projectivity -- V. Resolutions and Dimensions -- VI. Multi-Operational Holomorphic Calculus on the Taylor Spectrum -- VII. Flatness and Amenability -- Appendix A. Paracompact topological spaces -- Appendix B. Invariant means on locally compact groups -- Postscript -- ยง1. Extensions and derivations -- ยง2. Normal cohomology and its expression in terms of Ext -- ยง4. An interpretation of amenability-according-to-Connes in terms of the diagonal and reduced bifunctionals -- ยง5. โGeneral homologicalโ background to amenability according to Connes -- ยง6. Central contractibility (= central separability) and central cohomology -- ยง7. Homological dimensions. Results of a general character and results connected with the geometry of Banach spaces -- ยง8. Homological dimensions (continued). Algebras of smooth functions and some radical algebras -- ยง10. Homological dimensions (concluded). Connections with the question of an analytic structure on the spectrum -- ยง11. Miscellaneous results about the homological invariants of operator algebras and their modules -- ยง12. Completely bounded cohomology and its applications -- ยง13. Weakly amenable Banach algebras and various conditions for โordinaryโ and weak amenability -- ยง15. Some remarks about the development (and metamorphosis) of the problems of a multi-operator holomorphic calculus -- References -- Postscript references -- Index of terminology -- Index of notation and abbreviations

1. Mathematics
2. Category theory (Mathematics)
3. Homological algebra
4. Functional analysis
5. Algebraic topology
6. Mathematics
7. Functional Analysis
8. Category Theory
9. Homological Algebra
10. Algebraic Topology