Algebras of Linear Transformations This book studies algebras and linear transformations acting on finite dimensional vector spaces over arbitrary fields. It is written for students who have prior knowledge of algebra and linear algebra. The goal is to present a balance of theory and example in order for students to gain a firm understanding of the basic theory of finite dimensional algebras and to provide a foundation for subsequent advanced study in a number of areas of mathematics. As such the level of exposition is suitable for senior undergraduate students