This book describes recent research advances and computer tools that can be applied in the determination of geometric tolerances. A framework for tolerance synthesis is developed and used with artificial intelligence techniques to provide computer methods for both analysis and synthesis of geometric tolerance specifications. Tolerance primitives, based on a sound theory of tolerancing, are used to represent tolerance relationships or links between geometric entities and functional requirements. Algorithms are developed for the determination of boundedness and the measurement of sufficiency. A detailed constraint network is used to represent tolerance relations for a part under design and provide for the composition of tolerance specifications.