Preface -- Nomenclature -- 1 Complexes of Modules -- 1.1 Definitions and Basic Constructions -- 1.2 Complexes Formed from Modules -- 1.3 Free Complexes -- 1.4 Projective and Injective Complexes -- 1.5 Exercises -- 2 Short Exact Sequences of Complexes -- 2.1 The Groups Extn(C,D) -- 2.2 The Group ExtI(C,D) -- 2.3 The Snake Lemma for Complexes -- 2.4 Mapping Cones -- 2.5 Exercises -- 3 The Category K (R-Mod) -- 3.1 Homotopies -- 3.2 The Category K(R-Mod) -- 3.3 Split Short Exact Sequences -- 3.4 The Complexes Hom (C,D) -- 3.5 The Koszul Complex -- 3.6 Exercises -- 4 Cotorsion Pairs and Triplets in C(R-Mod) -- 4.1 Cotorsion Pairs -- 4.2 Cotorsion Triplets -- 4.3 The Dold Triplet -- 4.4 More on Cotorsion Pairs and Triplets -- 4.5 Exercises -- 5 Adjoint Functors -- 5.1 Adjoint Functors -- 5.2 Exercises -- 6 Model Structures -- 6.1 Model Structures on C(R-Mod) -- 6.2 Exercises -- 7 Creating Cotorsion Pairs -- 7.1 Creating Cotorsion Pairs in C(R-Mod) in a Termwise Manner -- 7.2 The Hill Lemma -- 7.3 More Cotorsion Pairs -- 7.4 More Hovey Pairs -- 7.5 Exercises -- 8 Minimal Complexes -- 8.1 Minimal Resolutions -- 8.2 Decomposing a Complex -- 8.3 Exercises -- 9 Cartan and Eilenberg Resolutions -- 9.1 Cartan-Eilenberg Projective Complexes -- 9.2 Cartan and Eilenberg Projective Resolutions -- 9.3 C-E Injective Complexes and Resolutions -- 9.4 Cartan and Eilenberg Balance -- 9.5 Exercises -- Bibliographical Notes -- Bibliography -- Index.