In recent years, non-rigid shapes have attracted growing interest, which has led to rapid development of the field, where the state-of-the-art sciences are very different - theory and numerical geometry, optimization, linear algebra, graph theory , machine learning and computer graphics, to name a few - is applied to find a solution. This book illustrates the current state of science in the analysis and synthesis of non-rigid shapes. A gallery of color photographs enhance the text. This book will appeal to graduate students, researchers and professionals in various fields of mathematics, computer science and engineering. It can be used to program in computer vision, numerical geometry and geometric modeling and computer graphics or for self-study.