A report by the Dept. of Defense¿s Command and Control Research Program. Contents: (1) Complexity in Natural and Economic Systems; (2) Concepts for Warfare from Complexity Theory; (3) Evidence for Complex Emergent Behavior in Historical Data; (4) Mathematical Modeling of Complexity, Knowledge, and Conflict; (5) An Extended Example of the Dynamics of Local Collaboration and Clustering, and Some Final Thoughts. Appendix: Optimal Control with a Unique Control Solution. Tables and figures.