Based on an introductory course on natural-language semantics, this book provides an introduction to type-logical grammar and the range of linguistic phenomena that can be handled in categorial grammar. It also contains work on categorial grammar and its application to natural-language semantics. The author chose the type-logical categorial grammar as his grammatical basis because of its broad syntactic coverage and its strong linkage of syntax and semantics. Although its basic orientation is linguistic, the book should also be of interest to logicians and computer scientists seeking connections between logical systems and natural language. Topics covered include higher-order logic, applicative categorial grammar, the Lambek calculus, co-ordination and unbounded dependencies, quantifiers and scope, plurals, pronouns and dependency, modal logic, intensionality, and tense and aspect. The book covers mathematical development; and an appendix includes the basic mathematical concepts used throughout the book.