The Lukasiewicz-Moisil algebras were created by Moisil as an algebraic counterpart for the many-valued logics of Lukasiewicz. The theory of LM-algebras has developed to a considerable extent both as an algebraic theory of intrinsic interest and in view of its applications to logic and switching theory. This book gives an overview of the theory, comprising both classical results and recent contributions, including those of the authors. N-valued and Theta-valued algebras are presented, as well as Theta-algebras with negation. Mathematicians interested in lattice theory or symbolic logic, and computer scientists, will find in this monograph stimulating material for further research.