This is a short course in which we start with the basic concepts of point set topology, and continue to homotopy and homology theories, and then manifolds, Riemannian Geometry, fiber bundles and complex manifolds. It is suitable for students in high energy physics and condensed matter physics. A good knowledge of mathemtical physics and group theory is necessary for this course.

These lecture notes are not complete and are being developed as I teach the course from time to time.

- Introduction to metric and topological spaces
- Homotopy groups
- Homology groups
- Manifolds
- Lie groups
- Cohomology theory
- Reimannian geometry
- Fiber bundles
- Connections in fibre bundles