This monograph arose from a collection of lectures on topics in finite rings at The University of Oklahoma. The motivation for preparing this survey was three-fold: (I) it was hoped that finite rings could provide a wealth of concrete and instructive examples for students mastering the first principles of ring theory and that this monograph could provide a supplementary text for a course in general ring theory; (II) for algebraists, this text provides a survey of the present state of the theory of finite rings with identity; (III) to provide a source material for the growing areas of discrete algebraic modeling.