Deductive Press

Introduction to Arithmetic Groups
Dave Witte Morris

ISBN: 978-0-9865716-0-2 (paperback)
           978-0-9865716-1-9 (hardcover)

photo of front cover This book provides a gentle introduction to the study of arithmetic subgroups of semisimple Lie groups. This means that the goal is to understand the group SL(n,Z) and certain of its subgroups. Among the major results discussed in the later chapters are the Mostow Rigidity Theorem, the Margulis Superrigidity Theorem, Ratner's Theorems, and the classification of arithmetic subgroups of classical groups. As background for the proofs of these theorems, the book provides primers on lattice subgroups, arithmetic groups, real rank and Q-rank, ergodic theory, unitary representations, amenability, Kazhdan's property (T), and quasi-isometries. Numerous exercises enhance the book's usefulness both as a textbook for a second-year graduate course and for self-study. In addition, notes at the end of each chapter have suggestions for further reading. (Proofs in this book often consider only an illuminating special case.) Readers are expected to have some acquaintance with Lie groups, but appendices briefly review the prerequisite background. A PDF file of the book is available on the internet. This inexpensive printed edition is for readers who prefer a hardcopy.

Download a free PDF file of this 492-page book by clicking HERE
(The PDF file has only 491 pages, but the official length of the book is 492 pages, because an extra page is added at the end for a barcode during the printing process.) 
The current version is 1.0 of April 2015.

The PDF has also been permanently archived at     (external links open in a new window)

The Latex source files are available at

Inexpensive printed copies of the book are also available.