ABSTRACT
This chapter presents several motivating examples of operator algebras and explains the precise definitions for a C*-correspondence and the various operator algebras associated with it. It also states the various gauge invariance uniqueness theorems of Katsura and others. The chapter describes a very general process for creating injective C*-correspondences from non-injective ones, without straying away from the associated Cuntz-Pimsner algebras (up to Morita equivalence). It presents a complete treatment (including proofs) for the C*-envelope of a unital operator space and describes various classification schemes for operator algebras coming from dynamical systems. The chapter discusses the topics of crossed products of arbitrary operator algebras. The chapter deals with local maps and gives the author an opportunity to apply the concepts and tools developed so far to an area of study that goes back to the early work of Barry Johnson.
