By the end of the course the student will know
- the concept of vector bundle and basic constructions about vector bundles,
- the basics of Stiefel-Whitney classes and some methods to compute them,
- the concept of oriented bundle and Euler class,
- the concept of complex structure on a real vector bundle,
- the basics of Chern classes and some methods to compute them,
- the basics of Pontrjagin classes and some methods to compute them,
- some geometric and topological applications of characteristic classes,
- the concept of Grassmann manifold and its importance for the classification of vector bundles.