Lecture 2: Fibrations
Lecture 3: Examples of Fibrations
Lecture 4: Towers of Fibrations and Spectral Sequences
Lecture 5: The Spectral Sequence of a 3-term Filtration
Lectures 6 and 7: The Spectral Sequence of a Filtered Complex and the Serre Spectral Sequence
Lecture 8: Examples: The Cellular Chain Complex and the Unitary Groups.
Lecture 9: The E^2 term of the Serre Spectral Sequence.
Lectures 10-11: Further examples and applications of the Serre Spectral Sequence.
Lecture 12: Cohomology.
Lectures 13-14: The Serre Spectral Sequence for cohomology and applications.
Lecture 15: Vector bundles and K-theory.
Lectures 16-17: Cohomology theories and the Atiyah-Hirzebruch Spectral Sequence.
Notes on principal bundles: These are notes (from a previous course) covering the classification of principal bundles, which will be needed for the proof of Bott Periodicity.
Lecture 18: The classification of principal U(n)-bundles. (A condensed version of the above notes.)
Lecture 19: The cohomology of BU.
Lectures 20-21: The Bott map and the homology of SU(n).
Lectures 22-23: Conclusion to the proof of Bott Periodicity.