Deformable objects are ubiquitous in the world, on all levels from micro to macro. Study and modeling of such shapes arises in a wide spectrum of applications, ranging from medicine to security. Non-rigid shapes have attracted a growing interest, leading to rapid development of the field, where state-of-the-art results from very different sciences - theoretical and numerical geometry, optimization, linear algebra, graph theory, machine learning and computer graphics, to mention several - are applied to find solutions. This book provides an overview of the current state of science in analysis and synthesis of non-rigid shapes. Everyday examples are used to illustrate and explain concepts and techniques. The presentation unfolds systematically, with numerous figures to enrich the exposition. Practice exercises follow at the end of each chapter, with detailed solutions to selected problems in the appendix. A gallery of color images enhances the text.