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This book provides an in-depth review of machine translation by discussing in detail a particular method, called compositional translation, and a particular system, Rosetta, which is based on this method. The Rosetta project is a unique combination of fundamental research and large-scale implementation. The book covers all scientifically interesting results of the project, highlighting the advantages of designing a translation system based on a relation between reversible compositional grammars. The power of the method is illustrated by presenting elegant solutions to a number of well-known translation problems. The most outstanding characteristic of the book is that it provides a firm linguistic foundation for machine translation. For this purpose insights from Montague Grammar are integrated with ideas developed within the Chomskyan tradition, in a computationally feasible framework. Great care has been taken to introduce the basic concepts of the underlying disciplines to the uninitiated reader, which makes the book accessible to a wide audience, including linguists, computer scientists, logicians and translators.