The present book addresses a number of specific topics in  computational number theory whereby the author is not attempting to be  exhaustive in the choice of subjects. The book is organized as  follows. Chapters 1 and 2 contain the theory and algorithms concerning  Dedekind domains and relative extensions of number fields, and in  particular the generalization to the relative case of the round 2 and  related algorithms. Chapters 3, 4, and 5 contain the theory and  complete algorithms concerning class field theory over number  fields. The highlights are the algorithms for computing the structure  of (Z_K/m)^*, of ray class groups, and relative equations for Abelian  extensions of number fields using Kummer theory. Chapters 1 to 5 form  a homogeneous subject matter which can be used for a 6 months to 1  year graduate course in computational number theory. The subsequent  chapters deal with more miscellaneous subjects. Written by an  authority with great practical and teaching experience in the field,  this book together with the author's earlier book will become the  standard and indispensable reference on the subject.

Advanced Topics in Computional Number Theory - Errata (2000) PDF

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