Conflict in the twenty-first century involves a complex interaction of variables. Equally complex are modern stability operations that occur concurrently or immediately following war or combat operations. This study examines planning methodology for stability operations, focusing on the specific doctrinal planning construct of "lines of operation," one of the "Elements of Operational Design" contained in the US Army's Field Manual 3-0, Operations. The monograph first traces the historiography of the term "lines of operations" and examines its development from an essential geographical principle of linear warfare to a cognitive tool for modern planners. Included in this analysis is an evaluation of military operational theory, general systems theory, emerging ideas associated with complexity theory, and problem solving constructs based on nonlinear principles. To evaluate the suitability of the lines of operation planning construct, the monograph examines a notional future case study involving the participation of US armed forces in a hypercomplex -multinational, joint, and interagency stability operation in the nation of Colombia. Colombia offers a feasible scenario because of the current diplomatic, economic, and military engagement, combined with a potential increase of all three areas in the near future. The case study develops two operational level courses of action; one applies the "lines of operation" construct, and the other applies a planning matrix, which considers the aspects of emerging theories and nonlinearity discussed in the monograph. The case study reveals that "lines of operations" is, and will continue to be, an enduring part of the military lexicon regarding the geographic orientation of an armed force. Additionally, as a planning construct, it is a useful method for visualizing and developing operational plans. However, when applied to hyper-complex operations, the suitability of "lines of operation" as a planning construct decreases relative to an increase in the amount of complexity present in the military problem. The monograph recommends the development of a holistic planning construct that merges current operational planning constructs-based on linear and nonlinear principles-with twenty-first century information-based tools and technology. Additional recommendations address steps to be taken in the areas of doctrine, training, and education, in order to improve the "lines of operations" planning construct and the overall approach to complex military problem solving at the operational level.