The rapid advance to the main theorems of class field theory which results from this approach has made it possible to include in this volume the most important consequences and elaborations, and further related theories, with the excep tion ...

The book contains the main results of class field theory and Artin L functions, both for number fields and function fields, together with the necessary foundations concerning topological groups, cohomology, and simple algebras.

The primary goal of the book was to give a rather complete presentation of algebraic aspects of global class field theory ... In this revised edition, two mathematical additions complementing the exposition of the original text are made.

Class field theory brings together the quadratic and higher reciprocity laws of Gauss, Legendre, and others, and vastly generalizes them. This book provides an accessible introduction to class field theory.

This book explores the consequences and the practical use of these results in detailed studies and illustrations of classical subjects. In the corrected second printing 2005, the author improves many details all through the book.

This book offers a modern exposition of the arithmetical properties of local fields using explicit and constructive tools and methods.

This book explores the consequences and the practical use of these results in detailed studies and illustrations of classical subjects. In the corrected second printing 2005, the author improves many details all through the book.

These are topological devices that take stock of all completions of a number eld at once.

This book offers a self-contained exposition of local class field theory, serving as a second course on Galois theory.

Almost self-contained, the book is accessible to any reader with a basic background in algebra and topological groups.