This book presents a theory of enriched meanings for natural language interpretation. Certain expressions that exhibit complex effects at the semantics/pragmatics boundary live in an enriched meaning space while others live in a more basic meaning space. These basic meanings are mapped to enriched meanings just when required compositionally, which avoids generalizing meanings to the worst case. The theory is captured formally using monads, a concept from category theory. Monads are also prominent in functional programming and have been successfully used in the semantics of programming languages to characterize certain classes of computation. They are used here to model certain challenging linguistic computations at the semantics/pragmatics boundary. Part I presents some background on the semantics/pragmatics boundary, informally presents the theory of enriched meanings, reviews the linguistic phenomena of interest, and provides the necessary background on category theory and monads. Part II provides novel compositional analyses of the following phenomena: conventional implicature, substitution puzzles, and conjunction fallacies. Part III explores the prospects of combining monads, with particular reference to these three cases. The authors show that the compositional properties of monads model linguistic intuitions about these cases particularly well. The book is an interdisciplinary contribution to Cognitive Science: These phenomena cross not just the boundary between semantics and pragmatics, but also disciplinary boundaries between Linguistics, Philosophy and Psychology, three of the major branches of Cognitive Science, and are here analyzed with techniques that are prominent in Computer Science, a fourth major branch. A number of exercises are provided to aid understanding, as well as a set of computational tools (available at the book's website), which also allow readers to develop their own analyses of enriched meanings.