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."

1. Basic Number Theory.- 2. Class Field Theory.- 3. Galois Groups.- 4. Abelian Fields.- 5. Artin L-Functions and Galois Module Structure.- Appendix 1. Fields, Domains, and Complexes.- 1.1. Finite Field Extensions.- 1.2. Galois Theory.- 1.3. Domains.- 1.4. Complexes.- Appendix 2. Quadratic Residues.- Appendix 3. Locally Compact Groups.- 3.1. Locally Compact Abelian Groups.- 3.2. Restricted Products.- Appendix 4. Bernoulli Numbers.- Tables.- References.- Author Index.

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

GPSR Compliance The European Union's (EU) General Product Safety Regulation (GPSR) is a set of rules that requires consumer products to be safe and our obligations to ensure this. If you have any concerns about our products you can contact us on ProductSafety@springernature.com. In case Publisher is established outside the EU, the EU authorized representative is: Springer Nature Customer Service Center GmbH Europaplatz 3 69115 Heidelberg, Germany ProductSafety@springernature.com