THE THEORY of convex figures and polyhedra provides an excellent example of a body of mathematical knowledge that offers theorems with elementary formulations and vivid geometric meaning. Despite this simplicity of formulation, the proofs are often not elementary. Thus the area presents a particular challenge to mathematicians, who have investigated convex figures and polyhedra for millenia, and yet have by far not exhausted the subject. Many of the theorems in this volume were in fact proved only a few years ago.