Title: Actions of automorphism groups of Lie groups,
Abstract: This is an expository article on properties of actions on Lie groups by
subgroups of their automorphism groups. After recalling various results on the
structure of the automorphism groups, we discuss actions with dense orbits,
invariant and quasi-invariant measures, the induced actions on the spaces of
probability measures on the groups, and results concerning various issues in
ergodic theory, topological dynamics, smooth dynamical systems, and probability
theory on Lie groups.