Differential Forms in Algebraic Topology

This text, developed from a first-year graduate course in algebraic topology, is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas - de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes - and include some applications to homotopy theory. By using the de Rham theory of differential forms as a prototype of cohomology, the machineries of algebraic topology are made easier to assimilate. This text should be suitable for self-study or for a one-term course in topology.