AT (Algebraic topology)
LNM0034 Bredon. Studies only the case of a finite group, but should give a good intro to the fundamental ideas and problems.
http://mathoverflow.net/questions/68330/is-the-equivariant-cohomology-an-equivariant-cohomology
http://sbseminar.wordpress.com/2010/04/26/equivariant-cohomology-wiki/
http://nlab.mathforge.org/nlab/show/equivariant+cohomology
The book of Jardine and Goerss, sections VI.3-4.
nLab page on Equivariant cohomology