Graduate Texts in Mathematics, 112. New York etc.: Springer-Verlag. XI, 326 p.; DM 78.00 (1987).

This book is unchanged from the first edition (by Addison-Wesley Publishing Company, 1973;

Zbl 0316.14001) except for the corrections of some misprints, and two items: 1. John Coates pointed out to me a mistake in chapter 21, dealing with the L-functions for an order. Hence I have eliminated the reference to orders at that point, and deal only with the absolute class group. - 2. I have renormalized the functions in chapter 19, following

*D. Kubert* and the author [in Math. Ann. 218, 61-96; 175-189; 273-285 (1975;

Zbl 0311.14005)]. Thus I use the Klein forms and Siegel functions as in that reference. Actually, the final formulation of Kroneckerâ€™s second limit formula comes out neater under this renormalization.