Part 3: Fiber Bundles

Principal bundles, associated bundles, frame bundle, and bundle classification

Connection 1-forms, curvature 2-forms, gauge transformations, and Yang-Mills equations

Chern classes, Pontryagin classes, Euler class, and the splitting principle

Chern-Weil homomorphism, invariant polynomials, Chern-Simons forms, and transgression