Introduction to Lie Groups
An MIT OpenCourseWare graduate course on Lie groups and their connections to differential geometry. The syllabus follows Sigurdur Helgason's textbook Differential Geometry, Lie Groups and Symmetric Spaces, drawing mainly on the first half of Chapter I and all of Chapter II, covering topics such as Lie algebras, the exponential map, homogeneous spaces, and the basics of Riemannian geometry that underpin the theory of symmetric spaces. Materials include lecture notes and problem sets used in the actual MIT class, free to access through OCW with no certificate offered. The course assumes strong background in manifolds and abstract algebra and is aimed at advanced undergraduates or beginning graduate students who want a rigorous entry point into semisimple Lie theory before tackling Helgason's fuller treatment of symmetric spaces.