ABSTRACT
This chapter introduces the notion of the algebra of a groupoid, a notion that would be extremely helpful in uncovering the properties of groupoids and their representation. First, the basic definitions and properties of associative algebras is discussed and a wealth of examples is shown. The chapter introduces the notion of linear representation of algebras that leads to the important notion of left-modules over the given algebra. It studies the basic properties of representations of algebras (or left-modules) and explores the relation between linear representations of algebras and linear representations of groupoids. The basic results regarding this relation is established. There are two natural representations of a groupoid, the regular representation and the fundamental representation. The chapter concludes by describing the fundamental representation.
