One of the major contemporary challenges in both physical and social sciences is modeling, analyzing, and understanding the self-organization, evolution, behavior, and eventual decay of complex dynamical systems ranging from cell assemblies to the human brain to animal societies. The multi-faceted problems in this domain require a wide range of methods from various scienti?c disciplines. There is no question that the inclusion of time delays in complex system models considerably enriches the challenges presented by the problems. Although this inclusion often becomes inevitable as real-world applications demand more and more realistic m- els, the role of time delays in the context of complex systems so far has not attracted the interest it deserves. The present volume is an attempt toward ?lling this gap. There exist various useful tools for the study of complex time-delay systems. At the forefront is the mathematical theory of delay equations, a relatively mature ?eld in many aspects, which provides some powerful techniques for analytical inquiries, along with some other tools from statistical physics, graph theory, computer science, dynamical systems theory, probability theory, simulation and optimization software, and so on. Nevertheless, the use of these methods requires a certain synergy to address complex systems problems, especially in the presence of time delays.

Amplitude Death, Synchrony, and Chimera States in Delay Coupled Limit Cycle Oscillators.- Delay-Induced Stability: From Oscillators to Networks.- Delay Effects on Output Feedback Control of Dynamical Systems.- Time-Delayed Feedback Control: From Simple Models to Lasers and Neural Systems.- Finite Propagation Speeds in Spatially Extended Systems.- Stochastic Delay-Differential Equations.- Global Convergent Dynamics of Delayed Neural Networks.- Stability and Hopf Bifurcation for a First-Order Delay Differential Equation with Distributed Delay.- Deterministic Time-Delayed Traffic Flow Models: A Survey.