This thesis concerns itself with the applicability of quantum field methods, in the fixed field approximation, to problems involving a weak gravitational field. After introducing general scattering relations, various classic problems are reviewed to illustrate various approaches to solving scattering problems. Newtonian and quantum mechanical field methods are illustrated using Coulomb scattering. Classical relativity is used to solve the bending of light rays by the sun. Finally, quantum field methods are used to solve the scattering of polarized photons by the sun. The additional problems of scattering of light by a mass distribution and by a rotating mass are calculable using this method.Science, Faculty ofPhysics and Astronomy, Departm...