Part (I) of this thesis is on the Cournot model. Our aDn has been to collect together the known results on the Cournot model, present them in a systematic manner and derive the results from a single set of postulates. In the process we have corrected some errors, generalised some results and discovered some new ones. Part (II) is a brief review of the two main approaches to oligopoly theory: (1) the Reaction Function approach (also known as the conjectural variations approach, the classical approach or the traditional approach); (2) the game-theoretic approach, particularly the Super-Game approach of James Friedman. We show that the Reaction Function approach leads either to inconsistency, or to implausible econom1C results. We show that the Super-Game approach of James Friedman suffers from several defects, notably lack of credibility. In Part (III) we develop a new approach to oligopoly theory that avoids the difficulties of the two standard approaches. We propose a concept of credibility that promises to reduce the number of a priori possible oligopoly solutions, thus strengthening the predictive power of the theory. (