Representation Theory is a branch of mathematics that studies how abstract algebraic structures, like groups and algebras, can be represented through linear transformations of vector spaces. This allows mathematicians to translate complex algebraic problems into more manageable linear algebra problems, making it easier to analyze their properties. In particular, representation theory is crucial in various fields, including physics, where it helps describe symmetries in quantum mechanics. By understanding how these algebraic structures act on vector spaces, researchers can gain insights into the underlying symmetries of physical systems and other mathematical phenomena.