In this third edition of the book, two new chapters have been added (case studies and steps to develop a profile, curve and surface) illustrating the applications of the methods developed in the book and demonstration of the methods to a practical problem. All the earlier chapters of the second edition have been completely rewritten and plenty of examples have been added to enhance understanding. The main aim of the book is to provide a good foundation of computer-aided geometric design (CAGD), the students of undergraduate (according to the US standard) courses in engineering – especially mechanical engineering, computer science, geometric modeling and CAD / CAM. It will also be useful to practicing engineers and professionals working in the aeronautical and space research and in the ship-building; car manufacturing and other areas requiring designing and fabrication of hulls, chassis and other engineering parts on a large scale; telephone set and mobile handset designing; washing machine and TV set designing; designer glassware industry; sport shoe upper designers; and so on. Reflecting the advances that have taken place in the study and applications of CAGD, this book treats not only the theory aspects but also deals with a broad variety of topics relating to the applications. CAGD is becoming a fast growing area, used in all kinds of manufacturing processes involving designing of geometric shapes (such as car chassis, telephones, satellites, missiles, trains etc) and in computer graphics. CAGD cannot be learnt without a sound knowledge of differential geometry. So, the book starts with a study of differential geometry, which is needed for a thorough understanding of CAGD. Since this book has been written mainly as a textbook for the undergraduate students of engineering institutes and colleges, the approach is lucid. Concepts introduced are always illustrated with examples, which are completely worked out. A list of problems is also given at the end of each chapter so that the students can apply their knowledge in solving them and thereby learn more.