  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.
