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I recommend Equivariant de Rham cohomology: theory and applications which in my opinion is a well-made introduction in equivariant cohomology. Moreover the article of Tymoczko "An introduction to equivariant cohomology and homology, following Goresky, Kottwitz, and MacPherson" in Snowbird lectures in algebraic geometry contains a lot of computations and examples of equivariant cohomology of GKM spaces.