Actions of Lie groups and Lie algebras on manifolds

Questions of the following sort are addressed:Does a given Lie group or Lie algebra act effectively on a given manifold? How smooth can such actions be? What fixed point sets are possible? What happens under perturbations?Old results are summarized and new ones presented, including: For every integer n there are solvable (in some cases, nilpotent) Lie algebras g that have effective smooth actions on all n-manifolds, but on some (in many cases, all) n-manifolds, g does not have effective analytic actions