London Mathematical Society Lecture Note Ser.: Algebraic Topology Via Differential Geometry by M. Karoubi and C. Leruste (1988, Trade Paperback)
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By Max Karoubi. Author Max Karoubi. Prerequisites are few since the authors take pains to set out the theory of differential forms and the algebra required. The reader is introduced to De Rham cohomology, and explicit and detailed calculations are present as examples.