Using tools from mathematical kinetic theory and stochastic game theory, this work deals with the modeling of large complex systems in the applied sciences, particularly those comprised of several interacting individuals whose dynamics follow rules determined by some organized, or even intelligent ability. Traditionally, methods of mathematical kinetic theory have been applied to model the evolution of large systems of interacting classical or quantum particles. This book, on the other hand, examines the modeling of living systems as opposed to inert systems. The author develops new mathematical methods and toolshopefully a new mathematicstoward the modeling of living systems. Such tools need to be far more complex than those dealing with systems of inert matter. Specific topics covered include: - Modeling of the competition between cells of an aggressive invasive agent and cells of the immune system; - Modeling of vehicular traffic flow; - Modeling of swarms and crowd dynamics in complex geometric environments; - Methodological aspects related to multiscale modeling of large systems viewed as interconnected subsystems. Modeling Complex Living Systems will be a valuable resource for applied mathematicians, engineers, physicists, biologists, economists, and graduate students involved in modeling complex social systems and living matter in general.