The first edition of this book provided the first systematic exposition
of the arithmetic theory of algebraic groups. This revised second
edition, now published in two volumes, retains the same goals, while
incorporating corrections and improvements, as well as new material
covering more recent developments. Volume I begins with chapters
covering background material on number theory, algebraic groups, and
cohomology (both abelian and non-abelian), and then turns to algebraic
groups over locally compact fields. The remaining two chapters provide a
detailed treatment of arithmetic subgroups and reduction theory in both
the real and adelic settings. Volume II includes new material on groups
with bounded generation and abstract arithmetic groups. With minimal
prerequisites and complete proofs given whenever possible, this book is
suitable for self-study for graduate students wishing to learn the
subject as well as a reference for researchers in number theory,
algebraic geometry, and related areas.