Lecture 1: definition of the higher homotopy groups, \pi_1 action, CW complexes, Whitehead’s Theorem (part 1)
Lecture 2: examples with nontrivial \pi_1 action, Whitehead’s Theorem (part 2), cellular approximation
Lecture 3: existence of CW approximations, Postnikov towers,
Lecture 4: a weak homotopy equivalence induces isomorphisms on homology/cohomology, excision (part 1)
Lecture 5: Freudenthal suspension, computation of \pi_n(S^n), introduction to stable homotopy
Lecture 6: excision (part 2)
Lecture 7: Hurewicz theorem (part 1)
Lecture 8: Hurewicz theorem (part 2), fiber bundles and fibrations (part 1)
Lecture 9: fiber bundles and fibrations (part 2), computations
Lecture 10: \omega spectra, cohomology from homotopy (outline), vector bundles, basic idea of characteristic classes
Lecture 11: cohomology of Grassmanians (statement), axioms for Steiffel-Whitney classes, operations on vector bundles
Lecture 12: cohomology from homotopy (proofs)