- Time and place: MWF 2.30-3.30, Science Center 411
- Instructor: Gereon Quick
- Office hours: Wednesday 1.30-2.30, Science Center 341 (or by appointment)
- Syllabus

- Lecture 1: Vector bundles
- Lecture 2: Vector bundles and sections
- Lecture 3: Families of sections
- Lecture 4: Constructing new bundles out of old
- Lecture 5: Euclidean bundles, orthogonal complements, and orientations
- Lecture 6: Stiefel-Whitney classes and embedding problems (Guest lecture by Mike Hopkins)
- Lecture 7: Stiefel-Whitney classes of projective spaces
- Lecture 8: Existence and uniqueness of Stiefel-Whitney classes I
- Lecture 9: Existence and uniqueness of Stiefel-Whitney classes II
- Lecture 10: The splitting principle and the projective bundle formula
- Lecture 11: The Grassmannian manifold and the universal bundle
- Lecture 12: Representability and vector bundles
- Lecture 13: Schubert cells and Schubert varieties
- Lecture 14: A cell decomposition for the Grassmannian
- Lecture 15: Cohomology of the Grassmannian
- Lecture 16: Chern classes for complex vector bundles
- Lecture 17: Complex K-theory
- Lecture 18: Complex K-theory as a representable functor
- Lecture 19: Complex K-theory as a cohomology theory
- Lecture 20: K-theory of complex projective spaces (Guest lecture by Mike Hopkins)
- Lecture 21: Splitting principle and the projective bundle formula in K-theory (Guest lecture by Mike Hopkins)
- Lecture 22: Thom classes and the Thom isomorphism in K-theory (Guest lecture by Mike Hopkins)
- Lecture 23: Proof of the Periodicity theorem I
- Lecture 24: Proof of the Periodicity theorem II
- Lecture 25: Adams operations in complex K-theory
- Lecture 26: The Hopf invariant one problem via K-theory
- Lecture 27: Applications of the Hopf invariant one problem
- Lecture 28: The Chern character
- Lecture 29: The e-invariant
- Lecture 30: The e-invariant and the J-homomorphism
- Lecture 31: The image of the J-homomorphism
- Lecture 32: The image of the J-homomorphism and Thom classes
- Lecture 33: Clifford algebras and vector fields on spheres (Guest lecturer: Mike Hopkins)
- Lecture 34: The image of J and the Adams conjecture
- Lecture 35: Sphere bundles and the Adams conjecture
- Lecture 36: Sullivan's proof of the Adams conjecture