| Lecture 1 | Up to 9.7 (definition of simplices) |
| Lecture 2 | Up to 18.7 (topological homotopy) |
| Lecture 3 | Up to 23.10 (exact sequences) |
| Lecture 4 | Up to 26.3 (Mayer-Vietoris for small cochains) |
| Lecture 5 | Up to 33.4 (Cohomology of products and coproducts) |
| Lecture 7 | Up to 47.10 (The Five Lemma) |
| Lecture 8 | Up to 50.12 (Cohomology of complex projective space) |
| Lecture 9 | Up to 54.5 (Relative and reduced cohomology) |
| Lecture 10 | Up to 58.6 (Partway through cohomology of U(n)) |
| Lecture 11 | Up to 60.8 (Hopf algebra structure for U(n)) |