The contents of this book originate from a collection of selected papers presented at the 9th CIRP International Seminar on CAT that was held from April 10-12, 2005 at Arizona State University, USA. The CIRP (Collège International pour la Recherche en Production or International Institution for Production Engineering Research) plans this seminar every two years, and the book is one in a series of Proceedings on CAT. The book is organized into seven parts: Models for Tolerance Representation and Specification, Tolerance Analysis, Tolerance Synthesis, Computational Metrology and Verification, Tolerances in Manufacturing, Applications to Machinery, and Incorporating Elasticity in Tolerance Models.