This book is addressed to all those - logicians, computer scientists, mathe maticians, philosophers of science as well as the students in all these disci plines - who may be interested in the development and current status of one of the major themes of mathematical logic in the twentieth century, namely the classical decision problem known also as Hilbert's Entscheidungsproblem. The text provides a comprehensive modern treatment of the subject, includ ing complexity theoretic analysis. We have ...