1 Cyclotomic Fields
1.1 Introduction
1.2 Herbrand-Ribet Theorem
1.3 The Cyclotomic Tower
1.4 The Main Conjecture
1.5 Iwasawa’s Theorem
2 Local Units
2.1 Introduction
2.2 Norm and Trace Operators
2.3 Interpolating Power Series
2.4 The Logarithmic Derivative
2.5 An Exact Sequence
2.6 The Higher Logarithmic Derivative Maps
3 Iwasawa Algebras and p-adic Measures
3.1 Introduction
3.2 p-adic Measures
3.3 The Mahler Transform
3.4 Restriction of Measures
3.5 The Fundamental Exact Sequence
3.6 Image of δk
4 Cyclotomic Units and Iwasawa’s Theorem
4.1 Introduction
4.2 p-adic Zeta Function
4.3 Cyclotomic Units
4.4 Iwasawa’s Theorem
4.5 Relation to the Main Conjecture
4.6 Another Property of Cyclotomic Units
4.7 Global Units
4.8 Ideal Class Groups
5 Euler Systems
5.1 Introduction
5.2 Euler Systems
5.3 Values of Euler Systems
5.4 The Factorization Theorem
5.5 An Application of the Cebotarev Theorem
6 Main Conjecture
6.1 Introduction
6.2 The Inductive Argument
6.3 Proof of the Main Conjecture