Redfield's theory and the theory of master equations have been reviewed and their applications to muonium spin dynamics discussed. It was found that both theories are equivalent in the Markov limit. In some cases, analytical expressions for relaxation rates are found. In addition, Redfield's theory was applied to describe spin relaxation of muonium-substituted free radicals near level-crossing resonances. Theoretical predictions were compared with experimental data for the C₆F₆-Mu radical and the results suggest there are several relaxation mechanisms involved. / Science, Faculty of / Physics and Astronomy, Department of / Graduate