The book was written primarily to research mathematicians who are interested in theoretical computer science and its connections with algebra and combinatorial theory. Similarly to other branches of theoretical computer science, the theory of (Mealy-type and Moore-type) automata is a basis of the technical achievements of computer science. Thus the present book may be useful for scientists working in a certain practical field. Although there are many books dealing with automaton theory, this work is the first one which is devoted to Moore-type automata particularly. One of the two “leitmotifs” of the book is the discussion of behavioural abilities of finite automata; the other is the question of most economical realization of a given behaviour. About the half of the work is based on the author's original articles and is not included in any book.