Nonlinear elasticity is concerned with nonlinear effects associated with deformations of elastic bodies subjected to external forces or temperature variations. It has important applications in, for example, the aerospace and rubber industries. It also underpins a number of the other disciplines such as biomechanics, particularly in connection with the mechanical behaviour of biological tissues, e.g. arteries. This book, written by a group of leading researchers invited especially for the purpose, provides an up-to-date and concise account of the fundamentals of the theory of nonlinear elasticity and a comprehensive review of several major current research directions in this important field. It combines the characteristics of coherence and detail found in standard treatises with the strength and freshness of research articles. The emphasis is placed firmly on coverage of modern topics and recent developments rather than on the very theoretical approach often found. The book will be an excellent reference source for both beginners and specialists in engineering, applied mathematics and physics. It is also ideally suited for graduate courses.