The proposal is focused on computational electromagnetics (CEM) with emphasis on the moment method (MoM) and its application to the numerical solution of integral equations (IEs) arising in electromagnetic (EM) scattering by either perfectly-conducting or homogeneous dielectric objects in both 2-D and 3-D geometries. Particularly it addresses four research objectives (ROs). RO1 concerns a priori and a posteriori error analyses for the Reduced Basis Method on account of its application to popular IEs in EM scattering theory (i.e. EFIE, MFIE, and CFIE). RO2 is aimed to shed light on the intimate (but quite involved) relationship between properties of the relevant integral operators underlying our preferred EM models and analogous properties of finite ranked operators resulting from their MoM discretization. This is expected to provide insights for performance and reliability improvements of common iterative techniques used to solve the corresponding MoM system (i.e. CG, BiCG, and GMRES). RO3 points to contribute to the development and further understanding of the approximation problem in the light of Enflo’s and subsequent work on the existence of Banach spaces lacking Grothendieck’s approximation property. This will be done in regard to the sole EFIE. The issue seems almost completely unexplored, yet, it may be useful to know if and when MoM intrinsically fails to represent certain classes of operators, commonly encountered in EM scattering, by finite ranked operators (e.g. depending on the smoothness of scatterers). This is the deepest theoretical theme addressed by the proposal and represents one of the strongest motivations that has led the fellow to apply at LJLL on the consideration of its researchers’ expertise on foundations of numerical methods. Finally RO4 regards numerical experimentation. It will aid the fellow in the development and testing of novel MoM-based schemes for EM scattering problems, but also in the refinement of existing analog techniques.