The numerical simulation of physical problems expressed in terms of partial differential equations (so-called PDE's) using a finite element, finite volume, boundary element, or any other numerical method requires the discretization of the domain of interrest into a set of elements, i.e. a mesh.

The differential equations are approximated by a set of algebraic equations on this mesh, this set being then solved to provide the approximate solution of the partial differential system over the field.

The discretization requires certain properties for the solution to be exploitable and must at least conform to all domain boundaries in order to accurately represent boundary conditions. Consequently, the mesh generation stage, as an essential pre-requisite, is of utmost importance in the computational schemes, as it is related to the convergence of the computational scheme as well as to the accuracy of the numerical solutions.

There is indeed a wide variety of algorithms suitable to produce such meshes. Some of these methods are designed to handle specific geometric situations while others can be used in a more general context. User-driven, semi-automatic as well as fully automatic methods exist leading to structured, unstructured or mixed meshes. The mesh generation problems are mainly related to the boundary meshing and domain meshing issues.

Numerous computational issues muste be carefully addressed for designing reliable and robust meshing algorithms. These issues concern computer-related data structures and algorithms as well as advanced data structures and computational schemes. In this regard, basic computational tools, geometric and dscrete geometric notions, computational and mesh data structures, element and mesh definitions are of significant importance.

The aim of this book is to provide a comprehensive survey of the different algorithms and data structures useful for triangulation and meshing construction. In addition, several aspects will also be described, for instance mesh modification tools, mesh evaluation criteria, mesh optimization, including even adaptative mesh constructions as well as parallel meshing techniques.