I am interested in topological group actions, particularly in free group actions, torsors, and characterization of principal bundles and conditions of their local triviality. Is there a good reference out there?
UPD: Even more specifically, I'm interested in the following questions:
1) What part of Husemoller's definition of principal bundle is important, e. g. are fibers of the bundle induced by a free action always homeomorphic to the group?
2) Are all principal bundles locally trivial? UPD: Not all, see local sections of closed subgroups of locally compact groups for examples. Are there known necessary conditions of them being locally trivial? UPD: Free action of a Lie group on a completely regular space is locally trivial iff it's Cartan, see the paper by Richard S. Palais.
3) Given a free action of a topological group $G$ on a topological space $X$, are there any known restrictions on topology of $X$ imposed by the topology of $X/G$? E.g. if it is known that $X/G$ is Hausdorff, compact or normal, what does it tell us about $X$?
UPD: this question on MO is very related: http://mathoverflow.net/questions/57015/which-principlal-bundles-are-locally-trivial