The book focuses on the dynamics of nonlinear oligopoly models. It discusses the classical Cournot model with a large variety of demand and cost functions that illustrate the many different types of possible best response functions and shows the existence of unique and multiple equilibria. Particular emphasis is placed on the influence of nonnegativity and capacity constraints. Dynamics are introduced under various assumptions for the adjustment process and the analysis of global dynamics is given through some specific examples. The book considers a range of oligopolies and gives conditions for the local asymptotic stability of their equilibria; the impact of constraints is also discussed. The book contains a number of technical appendices that summarize techniques of global dynamics not easily accessible elsewhere.