## About this book

### Introduction

From the reviews of the first printing, published as Volume 62 of the Encyclopaedia of Mathematical Sciences:

"... The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes."

Monatshefte fuer Mathematik, 1994

"... Koch's book is written mostly for non-specialists. It is an up-to-date account of the subject dealing with mostly general questions. Special results appear only as illustrating examples for the general features of the theory. It is supposed that the reader has good general background in the fields of modern (abstract) algebra and elementary number theory. We recommend this volume mainly to graduate studens and research mathematicians."

Acta Scientiarum Mathematicarum, 1993

### Keywords

Algebraische Zahlentheorie Galois Kohomologie Klassenkörpertheorie algebra algebraic number theory class field theory finite field galois cohomology number theory

#### Authors and affiliations

- 1.Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V.Arbeitsgruppe “Algebraische Geometrie und Zahlentheorie” an der Humboldt-Universität zu BerlinBerlinGermany

### Bibliographic information

## Reviews

From the reviews: "... The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes." Monatshefte fuer Mathematik, 1994 "... Number theory is not easy and quite technical at several places, as the author is able to show in his technically good exposition. The amount of difficult material well exposed gives a survey of quite a lot of good solid classical number theory... Conclusion: for people not already familiar with this field this book is not so easy to read, but for the specialist in number theory this is a useful description of (classical) algebraic number theory." Medelingen van het wiskundig genootschap, 1995