Algebraic Number Fields Second Edition

Subrings of fields
Complete fields
Decomposition groups and the Artin map
Analytic methods
Class field theory
Application of the general theory to quadratic fields
Appendix A. Normal basis theorem and Hilbert's theorem 90
Appendix B. Modules over principal ideal domains
Appendix C.Representation of permutation groups and Gauss Sums

This book contains an exposition of the main theorems of the class field theory of algebraic number fields. Familiarity with elementary Galois theory is presupposed. The text uses the structure theorem for finitely generated modules over a principal ideal domain, and the direct approach to the subject by convergence subgroups of the ideal group