Lays the foundation of a discrete event system theory which is shown to parallel the classical linear system theory. Commences with a focus upon areas of applications and relationships between graph theory, Petrinets and algebras followed by deterministic discrete event systems. The third part deals with stochastic discrete event systems. Concludes with open problems. Created within the text is a calculus which allows the derivation of analytical tools for computing the time behavior of this type of dynamic system.