| | | Preface | | |
| | | Introduction to Global Field Theory | | 1 |
| I | | Basic Tools and Notations | | 7 |
| 1 | | Places of K | | 9 |
| 2 | | Embeddings of a Number Field in its Completions | | 12 |
| 3 | | Number and Ideal Groups | | 21 |
| 4 | | Idele Groups - Generalized Class Groups | | 27 |
| 5 | | Reduced Ideles - Topological Aspects | | 45 |
| 6 | | Kummer Extensions | | 54 |
| II | | Reciprocity Maps - Existence Theorems | | 65 |
| 1 | | The Local Reciprocity Map - Local Class Field Theory | | 65 |
| 2 | | Idele Groups in an Extension L/K | | 91 |
| 3 | | Global Class Field Theory: Idelic Version | | 104 |
| 4 | | Global Class Field Theory: Class Group Version | | 125 |
| 5 | | Ray Class Fields - Hilbert Class Fields | | 143 |
| 6 | | The Hasse Principle - For Norms - For Powers | | 176 |
| 7 | | Symbols Over Number Fields - Hilbert and Regular Kernels | | 195 |
| III | | Abelian Extensions with Restricted Ramification - Abelian Closure | | 221 |
| 1 | | Generalities on H[subscript T][superscript S] / H[superscript S] and its Subextensions | | 221 |
| 2 | | Computation of A[subscript T][superscript S]:= Gal(H[subscript T][superscript S](p)/K) and T[subscript T][superscript S]:= tor[subscript Z[subscript p]] (A[subscript T][superscript S]) | | 240 |
| 3 | | Compositum of the S-split Z[subscript p]-Extensions - The p-Adic Conjecture | | 258 |
| 4 | | Structure Theorems for the Abelian Closure of K | | 274 |
| 5 | | Explicit Computations in Incomplete p-Ramification | | 342 |
| 6 | | Initial Radical of the Z[subscript p] - Extensions | | 348 |
| | More... | | |