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Chern - Weil homomorphism computes topological invariants of vector bundles and principal bundles on a given C^{\infty}-manifold via connection forms and curvature forms representing de Rham cohomology classes of the manifold. Considering the concepts connection and curvature, the theory becomes a bridge between algebraic topology and differential geometry. 

In the first of the seminar series we will present some preliminaries (vector bundles , connection and curvature on given vector bundle) for the theory.

References:

1. Shigeyuki Morita - Geometry of differential forms.
2. Loring W. Tu - Differential Geometry