  A new field of discrete differential geometry is presently emerging on the
border between differential and discrete geometry. Whereas classical
differential geometry investigates smooth geometric shapes (such as surfaces),
and discrete geometry studies geometric shapes with finite number of elements
(such as polyhedra), the discrete differential geometry aims at the development
of discrete equivalents of notions and methods of smooth surface theory.
Current interest in this field derives not only from its importance in pure
mathematics but also from its relevance for other fields like computer
graphics. Recent progress in discrete differential geometry has lead, somewhat
unexpectedly, to a better understanding of some fundamental structures lying in
the basis of the classical differential geometry and of the theory of
integrable systems. The goal of this book is to give a systematic presentation
of current achievements in this field.
