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Differential forms and cohomology.- Multiplicativity. The simplicial de rham complex.- Connections in principal bundles.- The chern-weil homomorphism.- Topological bundles and classifying spaces.- Simplicial manifolds. The chern-weil homomorphism for BG.- Characteristic classes for some classical groups.- The chern-weil homomorphism for compact groups.- Applications to flat bundles.- Errata.