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
CONTENT
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
