The book describes the physical and mathematical foundations, theory and methods for obtaining analytical solutions of electrodynamic problems in inhomogeneous l anisotropic media and shows their application to solving a wide range of three-dimensional and two-dimensional problems of electromagnetic zero. Conditions are derived under which vector electrodynamic equations are scalarized, i.e. reduced to two separate scalar electrodynamic problems with respect to potentials of electric and magnetic types, and the corresponding scalar electrodynamic partial differential equations of the second order are written out. Along the way, the issue of equivalent exciters of electromagnetic zero, important for general electrodynamics, is being considered.