Hossain, Ehsaan2015-09-182015-09-182015-09-182015http://hdl.handle.net/10012/9676This essay is meant to be an exposition of the theory of Leavitt path algebras and graph C*-algebras, with an aim to discuss some current classification questions. These two classes of algebras sit on opposite sides of a mirror, each reflecting aspects of the other. The majority of these notes is taken to describe the basic properties of Leavitt path algebras and graph C*-algebras, the main theme being the translation of graph-theoretic properties into exclusively (C*-)algebraic properties.enalgebragraphMaster ThesisPure Mathematics