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Representation theory (books) is the mathematical subfield that studies how algebraic structures—groups, Lie algebras, associative algebras, quivers and categories—can be realized concretely as linear transformations on vector spaces or modules. As a book category it spans introductory texts on group and linear representations, graduate-level treatments of Lie and associative algebra representations, and advanced monographs on topics such as quiver representations, category-theoretic and geometric representation theory, and applications to number theory, combinatorics, and mathematical physics. Typical readers range from advanced undergraduates and beginning graduate students seeking foundations to researchers looking for specialized theory or applications; related categories include abstract algebra, algebraic geometry, mathematical physics, and combinatorics.

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