I: Introduction -- II: A General Framework for Dynamic Economic Systems -- 1. Introduction -- 2. The Framework -- 3. Some Numerical Examples -- III: The General Theory of Set Valued Semidynamical Systems -- 1. A Set Valued Flow -- 2. The Space of Subsets -- 3. Semidynamical Systems for Set Valued Flows -- 4. Liapunov Functions -- IV: The Edgeworth Barter Process -- 1. Introduction -- 2. The Model -- 3. The Dynamics -- 4. Ex Post Pareto Optimality -- 5. Concluding Remarks -- V: Comparative Dynamics of Models of Adaptive and Optimal Economic Growth -- I. A Model of Adaptive Behavior -- II. Optimality of Adaptive Behavior -- Conclusion -- VI: The Structure of Optimality in Dynamic Models -- 1. Introduction -- 2. Adaptive and Optimal Programs -- 3. The Space of Trajectories -- 4. Optimal Control as a Set Valued Semidynamical System -- 5. Ex Ante Optimality -- 6. Ex Post Optimality -- 7. Dynamic Pareto Optimality -- 8. Asymptotic Optimality and Attraction -- 9. Concluding Remarks -- Glossary of Notation and Abbreviations -- Supplemental Bibliography.