**Introduction to Arithmetic
Groups**

Dave Witte Morris

ISBN: 978-0-9865716-0-2 (paperback)

978-0-9865716-1-9 (hardcover)

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.

http://arxiv.org/src/math/0106063/anc/ (external links open in a new window)

The Latex source files are available at

http://arxiv.org/abs/math/0106063

Inexpensive printed copies of the book are also available.

- The book is on Amazon
and Barnes and Noble, with the paperback priced at $14 (and the hardcover at about
$21 [Barnes and Noble] or $28 [amazon]) plus shipping (as of May 2023). It may also be available from
other online booksellers.

- The paperback and hardcover are both listed in
*Books in Print*, so your local bookstore should be able to special-order a copy for you from the distributor (Ingram Book Company). To cover their costs, the bookstore will probably need to charge a few dollars more than the above-mentioned online sellers. (At the industry-standard markup, the paperback would sell for about $20 and the hardcover for about $30.)

- Foreign readers: The paperback has been seen on amazon.co.uk for about £15, and on amazon.de for about €17.

**Errata**:

- page xii: The name of
**Hugh Thomas**is misspelled in line 7 of the acknowledgments. - page 109: A reference should have been given for Exercise 5.2#4. It is
Theorem 2 of [A. Borel, Density
and maximality of arithmetic subgroups,
*J. Reine Angew. Math.*224 (1966) 78-89. MR0205999]. (Thanks to Uri Bader for pointing out the omission.) - page 137: Change \(\mathrm{diag}(\omega, 1, \omega^{-1})\) to \(\mathrm{diag}(\omega, \omega^{-2}, \omega)\) in the last line. (Thanks to Sebastian Hurtado for pointing out the error.)
- page 147: Change \((A^\tau)^T A g = A\) to \((g^\tau)^T A g = A\) in line 2. (Thanks to Curt McMullen for pointing out the error.)