| Date | Topic |
| 1 | 1/26 | Overview of the material, curves |
| 2 | 1/31 | Surfaces and graphs |
| 2/02 | Level sets |
| 3 | 2/07 | The Implicit Functions Theorem |
| 2/09 | Regularity for curves |
| 4 | 2/14 | Tangent spaces and regular surfaces |
| 2/16 | Reparametrization of curves |
| 5 | 2/21 | Reparametrization of surfaces |
| 2/23 | Curves as graphs |
| 6 | 2/28 | Local Inversion, surfaces as graphs |
| 3/02 | Arc length, shortest curves and unit speed reparametrization |
| 7 | 3/07 | The first fundamental form |
| 3/09 | Midterm 1 |
| ☆ | | Spring Break |
| 8 | 3/21 | Introduction to areas and plane integrals |
| 3/23 | Double integrals, surface areas |
| 9 | 3/28 | Curvature of plane curves |
| 3/30 | The tangent angle, curvature of space curves |
| 10 | 4/04 | Torsion, the Frenet frame |
| 4/06 | Midterm 2 |
| 11 | 4/11 | The Frenet frame |
| 4/13 | The Darboux frame, geodesic and normal curvature |
| 12 | 4/18 | Geodesics |
| 4/20 | The shape operator |
| 13 | 4/25 | The second fundamental form |
| 4/27 | Principal curvatures |
| 14 | 5/02 | Gaussian curvature |
| 5/04 | Gauss' Theorema Egregium |
| ★ | 5/11 | Final Examination |