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. This book explores the consequences and the practical use of these results in detailed studies and illustrations of classical subjects. In the corrected second printing 2005, the author improves many details all through the book.

to Global Class Field Theory.- I. Basic Tools and Notations.- II. Reciprocity Maps - Existence Theorems.- III. Abelian Extensions with Restricted Ramification - Abelian Closure.- IV. Invariant Class Groups in p-Ramification - Genus Theory.- V. Cyclic Extensions with Prescribed Ramification.- §1 A General Approach by Class Field Theory.- §3 The General Case - Infinitesimal Knot Groups.- a) Infinitesimal Computations.- b) Infinitesimal Knot Groups - The Number of Relations - A Generalization of Šafarevi?'s Results.- Index of Notations.- General Index.