This book focuses on the interaction between the theoretical foundation of geometric modelling and practical applications in CAD and related areas. "Geometric Modelling: Theoretical and Computational Basis towards Advanced CAD Applications" starts with two position papers, discussing basic computational theory and practical system solutions. The seven review papers give a systematic overview of the current situation and deep insight for future research and development directions towards the reality of shape representation and processing. They discuss various aspects of important issues, such as geometric computation for space search and shape generation, parametric modelling, feature modelling, user interface for geometric modelling, geometric modelling for the next generation CAD, and geometric/shape standard. Other papers discuss features and new research directions in geometric modelling, solid modelling, free-form surface modelling, intersection calculation, mesh modelling and reverse engineering. They cover a wide range of geometric modelling issues to show the problem scope and the technological importance. Researchers interested in the status of geometric modelling research and developments should find this volume to be a useful reference.