This thesis contains three parts. In the first part, before getting into the discussion of magneto-optical properties for the systems under study, the author reviews some background subjects, such as the energy-band theory within the framework of density functional theory, the multiple scattering approach to the solution of band problem and its relation with the LMTO method, an account of the tight-binding LMTO method which we use exclusively in our calculations, the linear response theory and its application to the quantum theory of dielectric constants. In the second part, circular magnetic x-ray dichroism, as a powerful and newly developed experimental technique for quantitative study of the magnetic properties of different materials, is discussed. In the last part, the detailed study of the magneto-optical properties of some transition metals and the so-called half metallic Heusler alloys is presented.