I am doing a project on Hamiltonian group actions on symplectic manifolds, and my supervisor was able to list several good books on Riemannian geometry to start me off, but he didn't know of any single place to learn about Hamiltonian groups.

I have found some books (even available online from the author!) that come highly recommended, specifically: *Introduction to Symplectic and Hamiltonian Geometry, A. C. da Silva.*

As the title suggests however, this seems to come from more of a geometric standpoint. Which books are recommended that might focus on the group-theory and topology end of this subject? The project description specifically mentions cohomological obstructions, something that I think is related to group cohomology? (At this point I'm getting all of this from Wikipedia...)

I have had basic, introductory courses in Differential Geometry (in $\mathbb{R}^n$) and in topology (up to calculating the first fundamental group of a topological space).

Thank you in advance for any input!