Abstract:Brauer algebras are finite dimensional algebras. There is an explicit basis consisting of diagrams and a multiplication rule using concatenation of diagrams. Brauer algebras and closely related algebras are used in many areas of mathematics and mathematical physics, for instance to construct knot polynomials and in representation theory and invariant theory of orthogonal and symplectic groups. The latter connection is through orthogonal and symplectic Schur-Weyl duality, where Brauer algebras take the role played by group algebras of symmetric groups in classical Schur-Weyl duality. After explaining the definition of Brauer algebras and some ways to use them, their properties will be discussed, such as being semisimple, having finite global dimension and being self-injective or symmetric. Classifying Brauer algebras by these properties requires a variety of techniques in representation theory.