This classic book, originally published in 1968, is based on notes of a year-long seminar the authors ran at Princeton University. The primary goal of the book was to give a rather complete presentation of algebraic aspects of global class field theory, and the authors accomplished this goal spectacularly: for more than 40 years since its first publication, the book has served as an ultimate source for many generations of mathematicians.

In this revised edition, two mathematical additions complementing the exposition in the original text are made. The new edition also contains several new footnotes, additional references, and historical comments.

Readership

Graduate students and research mathematicians interested in number theory.

Reviews

"This new edition of the famous Artin-Tate notes on class field theory is a must-have, even for those who already have a copy of the original. This is a classic, a book that has inspired a generation of number theorists. Its hard going but deep, insightful, and essential."

-- MAA Reviews

Table of Contents

• Preliminaries
• The first fundamental inequality
• Second fundamental inequality
• Reciprocity law
• The existence theorem
• Connected component of idèle classes
• The Grunwald-Wang theorem
• Higher ramification theory
• Explicit reciprocity laws
• Group extensions
• Abstract class field theory
• Weil groups
• Bibliography