The Third Woodward Conference served as a forum for experts in numerous disciplines to discuss problems in modeling complex phenomena in both social and natural sciences. This volume contains both review articles and reports of recent research. Two recurrent themes are chaos and self-organized criticality. Among the topics covered in the volume are: general problems in the modeling of complex systems, such as machine learning of natural languages; nonlinear forecasting, with application, for example, to the arms race; chaotic dynamics and economics; modeling of complex phenomena in fluids; earthquake modeling and self-organized criticality; and mathematical models of complex patterns.