The interaction between ergodic theory and discrete groups has a
long history and much work was done in this area by Hedlund, Hopf
and Myrberg in the 1930s. There has been a great resurgence of
interest in the field, due in large measure to the pioneering work
of Dennis Sullivan. Tools have been developed and applied with
outstanding success to many deep problems. The ergodic theory of
discrete groups has become a substantial field of mathematical
research in its own right, and it is the aim of this book to
provide a rigorous introduction from first principles to some of
the major aspects of the theory. The particular focus of the book
is on the remarkable measure supported on the limit set of a
discrete group that was first developed by S. J. Patterson for
Fuchsian groups, and later extended and refined by Sullivan.
General
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