| Preface | p. v |
| Finite-dimensional modules | p. 1 |
| The Lie algebra sl Sl2and sl Sl2-modules | p. 1 |
| Classification of simple finite-dimensional modules | p. 5 |
| Semi-simplicity of finite-dimensional modules | p. 10 |
| Tensor products of finite-dimensional modules | p. 15 |
| Unitarizability of finite-dimensional modules | p. 17 |
| Bilinear forms on tensor products | p. 21 |
| Addenda and comments | p. 23 |
| Additional exercises | p. 26 |
| The universal enveloping algebra | p. 33 |
| Construction and the universal property | p. 33 |
| Poincaré-Birkhoff-Witt Theorem | p. 37 |
| Filtration on U(g) and the associated graded algebra | p. 41 |
| Centralizes of h and center of U(sl Sl2) | p. 44 |
| -Harish-Chandra homomorphism | p. 48 |
| Noetherian property | p. 50 |
| Addenda and comments | p. 52 |
| Additional exercises | p. 56 |
| Weight modules | p. 59 |
| Weights and weight modules | p. 59 |
| Verma modules | p. 62 |
| Dense modules | p. 68 |
| Classification of simple weight modules | p. 72 |
| Coherent families | p. 75 |
| Category of all weight modules with finite-dimensional weight spaces | p. 82 |
| Structure of $$$ in the case of one simple object | p. 85 |
| Structure of $$$ in the case of two simple, objects | p. 86 |
| Structure of $$$ in the case of three simple objects | p. 90 |
| Tensoring with a finite-dimensional module | p. 92 |
| Duality | p. 101 |
| Addenda and comments | p. 103 |
| Additional exercises | p. 108 |
| The primitive spectrum | p. 115 |
| Annihilators of Verma modules | p. 115 |
| Simple modules and central characters | p. 117 |
| Classification of primitive ideals | p. 119 |
| Primitive quotients | p. 121 |
| Centralizers of elements in primitive quotients | p. 124 |
| Addenda and comments | p. 128 |
| Additional exercises | p. 132 |
| Category O | p. 135 |
| Definition and basic properties | p. 135 |
| Projective modules | p. 139 |
| Blocks via quiver and relation | p. 144 |
| Structure of a highest weight category | p. 149 |
| Grading | p. 153 |
| Homological properties | p. 160 |
| Category of bounded linear complexes of projective graded D-modules | p. 164 |
| Projective functors on O0 | p. 170 |
| Addenda and comments | p. 178 |
| Additional exercises | p. 189 |
| Description of all simple modules | p. 195 |
| Weight and nonweight modules | p. 195 |
| Embedding into a Euclidean algebra | p. 197 |
| Description of simple nonweight modules | p. 201 |
| Finite-dimensionality of kernels and cokernels | p. 204 |
| Finite-dimensionality of extensions | p. 210 |
| Addenda and comments | p. 213 |
| Additional exercises | p. 215 |
| Categorification of simple finite-dimensional modules | p. 219 |
| Decategorification and categorification | p. 219 |
| Naïve categorification of V(n) | p. 221 |
| Weak categorification of V(n) | p. 226 |
| Categorification of V(n) via coinvariant algebras | p. 232 |
| Addenda and comments | p. 234 |
| Additional exercises | p. 237 |
| Answers and hints to exercises | p. 241 |
| Bibliography | p. 249 |
| Index of Notation | p. 255 |
| Index | p. 259 |
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