We give a brief overview of the current state of the study of the deformation
theory of Kleinian groups. The topics covered include the definition of the
deformation space of a Kleinian group and of several important subspaces; a
discussion of the parametrization by topological data of the components of
the closure of the deformation space; the relationship between algebraic
and geometric limits of sequences of Kleinian groups; and the behavior of
several geometrically and analytically interesting functions on the deformation
space.
Dedicated to David Epstein on the
occasion of his 60th birthday.
