Chapter I Group and Field Theoretic Foundations 1
1 Infinite Galois Theory 1
2 Profinite Groups 4
3 G-Modules 8
4 The Herbrand Quotient 12
5 Kummer Theory 14
Chapter II General Class Field Theory 18
1 Frobenius Elements and Prime Elements 18
2 The Reciprocity Map 21
3 The General Reciprocity Law 28
4 Class Fields 30
5 Infinite Extensions 32
Chapter III Local Class Field Theory 37
1 The Class Field Axiom 37
2 The Local Reciprocity Law 41
3 Local Class Fields 43
4 The Norm Residue Symbol over Qp 46
5 The Hilbert Symbol 50
6 Formal Groups 55
7 Fields of πn-th Division Points 60
8 Higher Ramification Groups 64
9 The Weil Group 69
Chapter IV Global Class Field Theory 72
1 Algebraic Number Fields 72
2 Ideles and Idele Classes 76
3 Galois Extensions 81
4 Kummer Extensions 86
5 The Class Field Axiom 89
6 The Global Reciprocity Law 90
7 Global Class Fields 96
8 The Ideal-Theoretic Formulation of Class Field Theory 102
9 The Reciprocity Law of Power Residues 110
Chapter V Zeta Functions and L-Series 113
1 The Riemann Zeta Function 113
2 The Dedekind Zeta Function 117
3 The Dirichlet L-Series 120
4 The Artin L-Series 121
5 The Equality of Dirichlet L-Series and Artin L-Series 128
6 Density Theorems 129
Literature 137
Index 139
