Introduction to Arithmetic Groups
by Dave Witte Morris

Click HERE for PDF file of the current draft.

Here are the contents of the current version:

Part I:
Introduction
1.
What is a locally symmetric space?
2.
Geometric meaning of R-rank and Q-rank
3.
Brief Summary


Part II:
Fundamentals
4.
Basic Properties of Lattices
5.
What is an Arithmetic Group?
6.
Examples of Arithmetic Groups
7.
SL(n,Z) is a Lattics in SL(n,R)


Part III:
Important Concepts
8.
Real Rank
9.
Q-rank
10.
Quasi-Isometries
11.
Unitary Representations
12.
Amenable Groups
13.
Kazhdan's Property (T)
14.
Ergodic Theory


Part IV:
Major Results
15.
Mostow Rigidity Theorem
16.
Margulis Superrigidity Theorem
17.
Normal Subgroups of Γ
18.
Arithmetic Subgroups of Classical Groups
19.
Construction of a Coarse Fundamental Domain
20.
Ratner's Theorems on Unipotent Flows



Appendixes
I.
Basic Facts about Semisimple Lie Groups
II.
Assumed Background
III.
A Quick Look at S-Arithmetic Groups
This version was posted in March 2014.  After minor revision, the final version should be available in the summer of 2014.

The Latex source files are available at http://arxiv.org/abs/math/0106063