| Week | Monday | Wednesday | Friday |
| 08/24 - 08/28 | Submanifolds of Eucl. space: definition and examples | Equivalent definitions for submanifolds; more examples | Implicit function theorem (IFT), inverse fct thm, parametrizations |
| 08/31 - 09/04 | Proof of IFT | Tangent spaces for submanifolds | Differentiability of maps between submanifolds |
| 09/07 - 09/11 | Labor day | Abstract manifolds: definitions and examples | Tangent spaces to manifolds |
| 09/14 - 09/18 | Tangent spaces: equivalent definitions | Derivations | Submanifolds |
| 09/21 - 09/25 | Regular values, Sard's theorem | Manifolds with boundary | Neat submanifolds, Retractions |
| 09/28 - 10/02 | Transversality; Embeddings into Eucl. space | Embeddings into Eucl. space | Degree mod 2 of maps |
| 10/05 - 10/09 | Partitions of unity | Approximation of continuous by smooth maps | Approximation of continuous by smooth maps, degree mod 2 revisited |
| 10/12 - 10/16 | Tangent bundle, vector bundles | Vector fields | Vector fields |
| 10/19 - 10/23 | Flow of a vectorfield; one-parameter group of diffeomorphisms | Covariant tensor product | No class - midterm exam |
| 10/26 - 10/30 | Class rescheduled | Exterior product | Covariant tensor bundles |
| 11/02 - 11/06 | Tensor fields and differential forms | Tensor fields and differential forms | Exterior derivative |
| 11/09 - 11/13 | Lie derivative | Orientations and volume forms | Orientations and volume forms |
| 11/16 - 11/20 | Integration on manifolds | Stokes' Theorem | No class - class rescheduled |
| 11/23 - 11/27 | Stokes' Theorem + applications | De Rham cohomology groups | Thanksgiving |
| 11/30 - 12/04 | The Brouwer degree | Introduction to Riemannian geometry | Introduction to Riemannian geometry |