The increase in the availability of 3D data comes with new challenges in terms of storage, classification, and retrieval of such data. The first challenge is the mathematical representation of the shape of objects. Second, almost every shape analysis task requires a measure that quantifies shape similarities and differences. The field of 3D shape analysis is being actively studied by researchers originating from at least four different domains: mathematics and statistics, image processing and computer vision, computer graphics, and medical imaging. This book provides an in-depth description of the major developments in the continuously expanding field of research. It can serve as a complete reference to graduate students, researchers, and professionals in different fields of mathematics, computer science, and engineering. The book could be used for courses of intermediate level in computer vision and computer graphics or for self-study.