Provides the reader with basic tools to solve problems of electromagnetism in thier natural functional frameworks thanks to modern mathematical methods: integral surface methods, and also semigroups, variational methods, etc. well adapted to a numerical approach. As examples of applications of these tools and concepts, we solve several fundamental problems of electromagentism, stationary or time-dependent: scattering of an incident wave by an obstacle, bounded or not, by gratings; wave propogation in a waveguide, with junctions and cascades. It is the aim to present mathematical notions that will allow a better understanding of modelization in electromagnetism and emphasize the essentail features related to the geometery and nature of materials.