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The Radiative Transfer (RT) Equation is solved for scattering systems using two Monte Carlo-based techniques. One calculates an effective scattering matrix for the systems; the other calculates the depth-resolved radiance distribution, neglecting polarization effects. The text opens by discussing the vector nature of electromagnetic radiation and how RT theory is modified to account for it. It goes on to describe the Monte Carlo methods used and some methods for simulating scattering systems. Finally, it discusses the results of calculations for several systems. Data are presented for both one- and two-layer systems (including polarization effects), the latter including a dielectric interface (both smooth and statistically roughened). The one-layer data are compared to well-known tabular data. Interface effects are studied, along with those of a reflecting bottom. Data are presented for two-layer systems in which the upper layer remains unchanged while the scattering function is varied for the lower layer. The depth-resolved radiance distribution, neglecting polarization effects, is presented and comparisons are made between single- and multiple-scattering calculations.