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 made an effort to combine the features of a research monograph and a textbook. Only the basic...