Includes bibliographical references.

Spectra and structure of ergodic actions -- Amenable actions, equivalence relations, and foliations -- Orbit equivalence and strong rigidity -- Cocycle superrigidity and the program to describe Lie group and lattice actions on manifolds -- Stabilizers of semisimple Lie group actions : invariant random subgroups -- Representations and arithmetic properties of actions, fundamental groups, and foliations -- Geometric structures : automorphisms of geometric manifolds and rigid structures ; locally homogeneous manifolds -- Stationary measures and structure theorems for Lie group actions.

"This volume of Robert J. Zimmer's selected papers, collected here for the first time, provides a rich context for his now-classic insights on group actions. The volume opens with a foreword by David Fisher, Alexander Lubotzky, and Gregory Margulis, as well as a substantial introductory essay by Zimmer himself, recounting the course of his career in mathematics. The volume closes with an article by Fisher on the most recent developments around the Zimmer program"--