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Group Representations is an important mathematics course, and is foundation to many other mathematics courses. It provides fundamental tools for studying group actions and group structures. It has important applications in mathematics, physics, chemistry, and many others. The course covers many topics: basic concepts of representations, and modules; Group rings, matrix algebras; Reducibility, and Maschke’s theorem; Schur’s Lemma and applications; Normal subgroups, and Clifford theorem; Tensor product; Character theory and its applications.