The Method of Moments (MoM) is deeply described and used for the analysis of electromagnetic (EM) radiation and scattering problems involving arbitrarily shaped 3D targets. The proposed MoM formulation allows us to investigate perfect and imperfect conductor, and dielectric object. Next, a novel method for efficient MoM analysis of electrically large objects using Characteristic Basis Functions (CBFs) is proposed to reduce the matrix solution time. The CBFs are special types of high-level basis functions, defined over the domains that encompass a relatively large number of conventional sub-domain bases, e.g., triangular patches or rooftops. This technique differs from other similar approaches developed previously, in several aspects. First, it includes mutual coupling effects directly by using primary and secondary CBFs, which are then used to represent the unknown induced currents on the blocks, and solved via the Galerkin method rather than using iterative refinements. Second, the Characteristic Basis Function Method (CBFM) is more general, and can be applied to a wide class of electromagnetic problems.