Written as an objective critical assessment, this book is the first linguistic theory guide to categorial grammars. Categorial grammars offer a radical alternative to the phrase-structure paradigm, with roots in the philosophy of language, logic, and algebra. Their historical evolution is outlined and their formal basis is discussed, beginning with a quasi-canonical core and including a number of possible extensions. Their treatment of a number of linguistic phenomena are also explored, including passives, raising, discontinuous dependencies and non-constituent coordination, as well as such general issues as word order, logic, psychological plausibility, and parsing. Chapters are as follows: Introduction (including underlying principles, practical basics, notational variants); A Brief History (including origins of the formalist enterprise, origins of categorical grammar); Classical Categorial Grammar: The Lambek Calculus (including associativity, composition, raising, division); Generalized Categorical Grammars (including extending the set of connectives, extending the set of rules); Current Practice (phonology, morphology, syntax); Current Issues (including semantics, word order, logic, complexity, parsing); and Overview and Prospect. The book is designed for students and researchers in current theories of grammar, including comparative, descriptive, and computational linguistics. It includes a name index, a categories index, and a subject index. Contains approximately 190 references. (LB)