The radiative transfer equations are solved for an electron-scattering stellar atmosphere as formulated by Chandrasekhar. The solution employs a transformation of the integro-differential form of the transfer equations into singular integral equations for the angular intensities of the radiation field. The Milne problem is solved to illustrate the method. In addition, the relationship is found between the above method of solution and Case's normal mode expansion method. This leads to an alternate procedure for finding the normal mode expansion coefficients. As an example of the method the constant, distributed source problem is solved for a half-space medium. / Master of Science