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This thesis develops dielectric theory in multilayers and following cases have been considered: - Normal incidence on a multilayered slab with n isotropic layers. - Parallel incidence on a multilayered slab with n isotropic layers. - Normal and parallel incidence on a multilayered with n anisotropic layers, analysed in the non-retarded limit. In each case we have developed the appropriate transfer matrix recurrence relation and solved it exactly, using computer algebra (REDUCE and MATHEMATICA) as an essential guide. For all the problems listed above, we have obtained closed form solutions for the dispersion relations of surface and interface plasmons and for the angle-resolved energy-loss function. The energyloss spectrum is then obtained by integrating over wavevectors. The formulas we have derived are applied to real materials such as Al/Mg, Al/Al203, Al/Si02/Si, diamond and graphite.