| Preface | 8 |
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| Nomenclature | 10 |
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| 1 Complexes of Modules | 14 |
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| 1.1 Definitions and Basic Constructions | 14 |
| 1.2 Complexes Formed from Modules | 17 |
| 1.3 Free Complexes | 19 |
| 1.4 Projective and Injective Complexes | 20 |
| 1.5 Exercises | 24 |
| 2 Short Exact Sequences of Complexes | 26 |
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| 2.1 The Groups Extn(C,D) | 26 |
| 2.2 The Group Ext1(C,D) | 29 |
| 2.3 The Snake Lemma for Complexes | 35 |
| 2.4 Mapping Cones | 37 |
| 2.5 Exercises | 38 |
| 3 The Category K (R-Mod) | 40 |
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| 3.1 Homotopies | 40 |
| 3.2 The Category K(R-Mod) | 41 |
| 3.3 Split Short Exact Sequences | 43 |
| 3.4 The Complexes Hom (C,D) | 46 |
| 3.5 The Koszul Complex | 48 |
| 3.6 Exercises | 49 |
| 4 Cotorsion Pairs and Triplets in C(R-Mod) | 50 |
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| 4.1 Cotorsion Pairs | 50 |
| 4.2 Cotorsion Triplets | 55 |
| 4.3 The Dold Triplet | 57 |
| 4.4 More on Cotorsion Pairs and Triplets | 58 |
| 4.5 Exercises | 61 |
| 5 Adjoint Functors | 62 |
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| 5.1 Adjoint Functors | 62 |
| 5.2 Exercises | 67 |
| 6 Model Structures | 68 |
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| 6.1 Model Structures on C(R-Mod) | 68 |
| 6.2 Exercises | 77 |
| 7 Creating Cotorsion Pairs | 79 |
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| 7.1 Creating Cotorsion Pairs in C(R-Mod) in a Termwise Manner | 79 |
| 7.2 The Hill Lemma | 80 |
| 7.3 More Cotorsion Pairs | 85 |
| 7.4 More Hovey Pairs | 88 |
| 7.5 Exercises | 89 |
| 8 Minimal Complexes | 91 |
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| 8.1 Minimal Resolutions | 91 |
| 8.2 Decomposing a Complex | 94 |
| 8.3 Exercises | 95 |
| 9 Cartan and Eilenberg Resolutions | 96 |
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| 9.1 Cartan–Eilenberg Projective Complexes | 96 |
| 9.2 Cartan and Eilenberg Projective Resolutions | 98 |
| 9.3 C–E Injective Complexes and Resolutions | 101 |
| 9.4 Cartan and Eilenberg Balance | 102 |
| 9.5 Exercises | 102 |
| Bibliographical Notes | 104 |
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| Bibliography | 106 |
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| Index | 108 |
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