This new volume introduces readers to some of the current topics of research in the geometry of polyhedral surfaces, with applications to computer graphics. It provides a systematic introduction to the geometry of polyhedral surfaces based on the variational principle. This new volume introduces readers to some of the current topics of research in the geometry of polyhedral surfaces, with applications to computer graphics. The main feature of this volume is a systematic introduction to the geometry of polyhedral surfaces based on the variational principle. The authors focus on using analytic methods in the study of some of the fundamental results and problems of polyhedral geometry: for instance, the Cauchy rigidity theorem, Thurston's circle packing theorem, rigidity of circle packing theorems, and Colin de Verdiere's variational principle. This present book is the first complete treatment of the vast, and expansively developed, field of polyhedral geometry.