Generalized representation theorems are developed for electromagnetic diffraction in a domain which is arbitrarily divided into two or more different regions. Each region has different electromagnetic parameters and is assumed to be linear, homogeneous, isotropic, and of finite conductivity. The theorems apply to any harmonic input source without imposing any restrictions on the geometry of the diffracting surfaces. The total diffracted field can be expressed in terms of three newly introduced quantities: a geometrical factor matrix for each diffracting surface, a propagation matrix for each region, and an interaction matrix between two adjacent surfaces. The resultant solution is in an integral matrix form which can be evaluated either analytically or numerically depending upon the complexity of the geometry. The solution can be reduced to a simpler one for a smooth scatterer on whose surface the radii of curvature are longer than the source wavelength. Both the two- and three-dimensional forms of the representation theorems are formulated and specifically developed in a cylindrical coordinate system for cylindrical diffracting surfaces. The present formulation can be applied to detailed studies on the effects of a half-space, surface topography, a weathering layer, and a disseminated ore zone surrounding the main deposit; these geometries occur in almost all practical mineral environments.