Nonclassical logics play an ever-increasing role in various disciplines from mathematics, informatics and computer science to artificial intelligence, cognitive science, linguistics and philosophy. The authors develop a uniform framework of relational semantics to mediate the connection between logical calculi and their semantics through algebra, resulting in a lucid and conceptually clear presentation. Among the familiar logics covered are normal modal logics such as K and S5 as well as substructural logics such as relevance logics, linear logic and Lambek calculi. Less-familiar and new logical systems are treated with equal deftness. Suitable for use as a graduate textbook in nonclassical logic, this book will also please experts with gems such as the chapter on topological duality theory. Even novices can find their way eased into the field by an appendix that provides a concise introduction into the relevant parts of universal algebra. Book jacket.