| Wk | Date | Topics |
| 1 | 9/02 | Introduction, intuitive notions |
| 2 | 9/07 | Review of basic set theory |
| 9/09 | Distances, open sets in metric spaces |
| 3 | 9/14 | Continuity in metric spaces, topological spaces |
| 9/16 | Basis of a topology |
| 4 | 9/21 | Comparisons, order topologies |
| 9/23 | Product topologies |
| 5 | 9/28 | Subspace topologies |
| 9/30 | Closed sets |
| 6 | 10/05 | Neighborhoods, accumulation points |
| 10/07 | Hausdorff spaces, separation properties |
| 7 | 10/12 | Continuous functions, homeomorphisms |
| 10/14 | The language of categories |
| 8 | 10/19 | Fall Break |
| 10/21 | The category $\operatorname{Top}$ |
| 9 | 10/26 | Midterm - Take-home component |
| 10/28 | Topologies on general products |
| 10 | 11/02 | Metric topoloogies revisited |
| 11/04 | The uniform topology |
| 11 | 11/09 | Sequential characterizations and uniform convergence |
| 11/11 | Connectedness |
| 12 | 11/16 | Connectedness, continued |
| 11/18 | Path connectedness |
| 13 | 11/23 | Compactness |
| 11/25 | Thanksgiving Break |
14 | 11/30 | Compactness in metric spaces |
| 12/02 | Local compactness and compactification |
15 | 12/07 | Nets. Urysohn's Metrization Theorem |
| 12/09 | Introduction to Algebraic Topology |