Geometry of Manifolds
An advanced graduate topology and geometry course from MIT OpenCourseWare covering differentiable manifolds, vector fields, and differential forms. The syllabus builds up Lie groups, the de Rham theorem, and Riemannian manifolds, tracing how local calculus tools extend to curved, coordinate-free spaces. Materials include MIT's lecture notes, problem sets, and readings that assume a solid background in point-set topology and linear algebra. There are no video lectures, but the course pages lay out the full sequence of topics and assignments as taught at MIT, letting a self-directed student work through the same material as enrolled students. As with all MIT OpenCourseWare offerings, the content is free to access and reuse under a Creative Commons license, with no certificate or instructor feedback attached.