In this report we present the mathematical foundations of the physical processes for true in-situ retorting by electromagnetic heating. The modeling of in-situ retorting via electromagnetic heating requires a mathematical formulation of the problem and empirical relations for such quantities as thermal conductivity, heat capacities, rate constants, permeabilities, and viscosities. The mathematical formulation consists of equations for conservation of species, saturations, capillary pressure, momentum and energy. These equations constitute a system of coupled non-linear partial differential equations which must be solved numerically. 8 references.