This monograph requires basic knowledge of the variational theory of elliptic PDE and the techniques used for the analysis
of the Finite Element Method. However, all the tools for the analysis of FEM (scaling arguments, finite dimensional estimates
in the reference configuration, Piola transforms) are carefully introduced before being used, so that the reader does not
need to go over longforgotten textbooks. Readers include: computational mathematicians, numerical analysts, engineers and
scientists interested in new and computationally competitive Discontinuous Galerkin methods. The intended audience includes
graduate students in computational mathematics, physics, and engineering, since the prerequisites are quite basic for a second
year graduate student who has already taken a non necessarily advanced class in the Finite Element method.