An emerging field of discrete differential geometry aims at the development of discrete equivalents of notions and methods of classical differential geometry. The latter appears as a limit of a refinement of the discretization. Current interest in discrete differential geometry derives not only from its importance in pure mathematics but also from its applications in computer graphics, theoretical physics, architecture, and numerics. Rather unexpectedly, the very basic structures of discrete differential geometry turn out to be related to the theory of integrable systems. One of the main goals of this book is to reveal this integrable structure of discrete differential geometry. For a given smooth geometry one can suggest many different discretizations. Which one is the best? This book answers this question by providing fundamental discretization principles and applying them to numerous concrete problems. It turns out that intelligent theoretical discretizations are distinguished also

Review

"This book gives new life to old concepts of classical differential geometry, and a beautiful introduction to new notions of discrete integrable systems. It should be of interest to researchers in several areas of mathematics (integrable systems, differential geometry, numerical approximation of special surfaces), but also to advanced students interested in a good introduction to several classical areas of mathematics. Parts of it could well be used for graduate or possibly advanced undergraduate courses in mathematics." ---- Mathematical Reviews

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