This title presents a basis for the theory of the mu-calculus, considered as an algebraic system, rather than a logic. The subject is presented in a unified way, and in a form as general as possible. Therefore, the emphasis is on the generality of the fixed-point notation, and on the connections between mu-calculus, games, and automata. This book should be accessible for graduate or advanced undergraduate students both in mathematics and computer science. It is designed especially for researchers and students interested in logic in computer science, computer aided verification, and general aspects of automata theory, and aimed at gathering in a single place the fundamental results of the theory, often hardly accessible for interested readers. The presentation is self-contained, except for the proof of the Mc-Naughton's Determinization Theorem. However, it is supposed that the reader is already familiar with some basic automata theory and universal algebra.