This classic book gives a thorough introduction to constructive algebraic number theory, and is therefore especially suited as a textbook for a course on that subject. It also provides a comprehensive look at recent research. For experimental number theoreticians, the authors developed new methods and obtained new results of great importance for them. Both computer scientists interested in higher arithmetic and those teaching algebraic number theory will find the book of value.

Computational algebraic number theory has been attracting broad interest in the last few years due to its potential applications in coding theory and cryptography. For this reason, the Deutsche Mathematiker Vereinigung initiated an introductory graduate seminar on this topic in Dusseldorf. The lectures given there by the author served as the basis for this book which allows fast access to the state of the art in this area. Special emphasis has been placed on practical algorithms - all developed in the last five years - for the computation of integral bases, the unit group and the class group...