Includes Bibliography

1. On the Reduction Theory of Quadratic Forms
2.Reduction of Quadratic Forms, According to Minkowski and Siegel
3. Groups of Indefinite Quadratic Forms and Alternating Bilinear Forms
4. Discontinuous Subgroups of Classical Groups
5. Fundamental Sets for Arithmetic Groups
6. Fundamental Domains of Arithmetic Groups

Arithmetic subgroups of Lie groups are a natural generalization of SL(n,Z) in SL(n,R)

and play an important role in the theory of automorphic forms and the theory of moduli spaces in algebraic geometry and number theory through locally symmetric spaces associated with arithmetic subgroups. One key component in the theory of arithmetic subgroups is the reduction theory which started with the work of Gauss on quadratic forms.

This book consists of papers and lecture notes of four great contributors of the reduction theory: Armand Borel, Roger Godement, Carl Ludwig Siegel and André Weil. They reflect their deep knowledge of the subject and their perspectives. The lecture notes of Weil are published formally for the first time, and other papers are translated into English for the first time. Therefore, this book will be a very valuable introduction and historical reference for everyone interested in arithmetic subgroups and locally symmetric spaces.

A publication of Higher Education Press (Beijing). Exclusive rights in North America; non-exclusive outside of North America. No distribution to mainland China unless order is received through the AMS bookstore. Online bookstore rights worldwide. All standard discounts apply.