| Wk | Date | Topics |
| 1 | 1/25 | Overview of the material, curves |
| 2 | 1/30 | Surfaces and graphs |
| 2/01 | Level sets, implicit functions |
| 3 | 2/06 | Regularity for curves |
| 2/08 | Tangent spaces and regular surfaces |
| 4 | 2/13 | Curves and the tangent space, the Chaine Rule |
| 2/15 | Reparametrization, the Gauss Map |
| 5 | 2/20 | Local inversion, curves and surfaces as graphs |
| 2/22 | Arc length |
| 6 | 2/27 | Shortest curves and unit speed reparametrization |
| 2/29 | The first fundamental form |
| 3/02 | Extra session: The Implicit Functions Theorem |
| 7 | 3/05 | Midterm 1 |
| 3/07 | Surface areas |
| 8 | | Spring Break |
| 9 | 3/19 | Curvature of plane curves |
| 3/21 | The tangent angle, curvature of space curves |
| 10 | 3/26 | Torsion, the Frenet frame |
| 3/28 | Frenet formulas |
| 11 | 4/02 | The Darboux frame, geodesic and normal curvatures |
| 4/04 | Properties of the normal curvature |
| 12 | 4/09 | The shape operator |
| 4/11 | Midterm 2 |
| 13 | 4/16 | The second fundamental form |
| 4/18 | Principal curvatures |
| 14 | 4/23 | The type of a surface |
| 4/25 | Gaussian curvature |
| 15 | 4/30 | Theorema Egregium |
| 5/02 | Isometries | |
| 🎓 | 5/08 | Final examination |