It is the purpose of this thesis to present a study of the conflicting aspects of the two major twentieth-century cosmological theories, the Steady State Theory and the Evolutionary Theory. Further, the study was directed toward a decision as to which of the two is the more plausible solution in the light of recent astronomical discoveries. The method employed involved a detailed study of each theory and its historical background, primary postulates, and the contributions of its major proponents. Prior to the presentation of each theory, both a discussion of the structure of the known physical universe and a survey of the pioneer cosmological theories of the twentieth century were included as a means of providing historical perspective. Thr...