This book (composed of 2 volumes) introduces the notions and concepts at the basis of geometric modeling problems, triangulation and mesh in the application framework numerical simulations. First, the basic geometric elements, seen as interpolating from Lagrange or Bezier, are described. Then various problems related to triangulations and geometric modeling are addressed, in order to go from a continuous model to a discrete model and vice versa. The notion of metric is introduced and discussed, metrics being the natural way to assess the quality of geometric elements and triangulations as...