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

Class field theory, which is so immediately compelling in its main assertions, has, ever since its invention, suffered from the fact that its proofs have requir

Translation of the French Edition

Global class field theory is a major achievement of algebraic number theory based on the functorial properties of the reciprocity map and the existence theorem.

A self-contained exposition of local class field theory for students in advanced algebra.