Theoretical models of simple computing mahcines, known as automata, play a central role in theoretical computer science. This textbook presents an introduction to the theory of automata and to their connections with the study of languages. At the heart of the book is the notion that by considering a language as a set of words it is possible to construct automata which `recognize' words in the language. Consequently one can generate a correspondence between a hierarchy of machines and a corresponding hierarchy of grammars and languages. Professor Howie leads the reader from finite state automata through pushdown automata to Turing machines. He demonstrates clearly and elegantly the fundamental connections between automata and abstract algebra via the notions of syntactic monoid and minimal automaton. The author presupposes a basic familiarity with modern algebra, but beyond this the book is self-contained. As a result, the book will make ideal reading for students of mathematics and computer science approaching this subject for the first time.