Our purpose in writing this book is to present a universal theory of automata which on one hand unifies the theories of several well-known types of automata and on the other hand allows interesting new applications and results. The frame work for our development is category theory, especially universal constructions in monoidal categories. But we will carefully motivate and introduce all those (and only those) notions and results of category theory which are needed in our approach. The reader is only assumed to be familiar with sets, deterministic functions, relations and the basic no tions...