This document provides an outline and overview of concepts in signal processing and representation theory, including: - Algebra review covering numbers, groups, vector spaces, inner product spaces, and orthogonal/unitary operators. - Representation theory, including orthogonal/unitary representations that map groups to transformations on inner product spaces, and irreducible representations that cannot be broken into smaller representations. - Examples of representations including rotations/reflections on vector spaces and groups of matrices represented on spaces of arrays. The document reviews key algebraic concepts as background for representation theory and its applications in signal processing.