A traditional course in abstract algebra often offers little motivation for students whose primary interest lies outside of pure mathematics. One way to involve these students is through a course that includes topics in discrete mathematics along with substantial and interesting applications of algebra. This text outlines such a course. It offers applications not usually available in conventional algebra texts. Congruences and homomorphisms of groups, rings, and universal algebras are covered because of the importance of congruence in the theory of machines and its natural extension to congruence of universal algebra. In fact, congruence relations provide a unifying theme for many of the seemingly disparate topics that are treated.