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This thesis attempts to answer the following research questions: "What are the concepts and principles of a targeting theory based on Complexity theory?" "What are the principles and concepts of Complexity theory?" "What insights does Complexity theory provide for the military strategist?" Finally it asks, "What are the targeting implications for the war on terrorism using a Complexity-based targeting theory?" To answer these questions the study reviewed the literature of Systems, Chaos and Complexity theory that traces the broad historical sequence of systems theoretical thought and development. Information gained in this review was used to describe and explain each theory's main terms, concepts and principles and to establish a foundation for the targeting theory and its application to radical Islamic terrorism. This information was also used to explore the impact of nonlinear system theory as applied to conceptual thinking about warfare.