Introduction to Representation Theory
Representation theory studies how groups, Lie algebras, and associative algebras act on linear spaces, translating abstract symmetry into matrices and linear transformations. This MIT OpenCourseWare course covers representations of finite groups, group algebras, representations of quivers, and structure theory of associative algebras, building toward Lie algebras and their representations. Materials include lecture notes, problem sets, and readings drawn from the course as taught at MIT, aimed at undergraduates who already know linear algebra and abstract algebra. The course builds concepts from basic examples like symmetric groups toward general structural results such as Maschke's theorem and Wedderburn's theorem, giving a first rigorous pass through a subject that underlies much of modern algebra and mathematical physics. As with other MIT OpenCourseWare offerings, all materials are free to access and there is no certificate.