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This book elaborates the concept of probabilistic and photometric invariants for radiation fields of a homogeneous slab bounded below by a horizontally uniform bottom, combining the intensities in mirror upgoing and downgoing viewing directions at two current mirror-symmetrical or arbitrary optical levels of a homogeneous slab, based on the mirror reflection principle introduced by the author. Exact linear and nonlinear Fredholm integral equations of the second kind as well as linear singular integral equations with Couchy-type kernels have been obtained, their solutions being invariant relative to optical depth shifts with simultaneous rotation of viewing lines. The solution domains of these equations regarding the slab's optical thicknesses and intervals of acting angular variables as well as the computation times can be decreased by more than two times in comparison with non-symmetrized solutions of initial boundary problems. The influence of underlying surfaces at the lower boundary of a homogeneous slab on the values of probabilistic and photometric invariants has been accounted for. To construct new objects of radiative transfer theory (unified probabilistic and photometric functions for scattered photons exiting the medium), the author has modified classical Ambartsumian-Chandrasekhar's principles of invariance, transformed the respective structural functions of radiative transfer theory, and improved the Gauss-Seidel method for numerical radiation modeling, including its calibration and information compression of its end results.