On Borel equivariant cohomology:
Loring Tu, What is… Equivariant Cohomology?, Notices of the AMS, Volume 85, Number 3, March 2011 (pdf, pdf)
Loring Tu, Introductory Lectures on Equivariant Cohomology, Annals of Mathematics Studies 204, AMS 2020 (ISBN:9780691191744)
On differential forms in algebraic topology:
On differential geometry with focus on Chern-Weil theory:
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