"The objective of this research project is to develop a comprehensive mathematical framework to analyze and optimize future complex systems characterized by their large dimensions, their stochastic aspects, and their being self-organized, such as smart grids and small cell telecommunication networks.Complex systems are inherently not tractable by existing mathematical tools due to their large physical dimensions and to their many stochastic parameters.In the past decades, several mathematical tools have emerged that enable the analysis of simplified models of complex systems. Among those tools, we mention importantly large dimensional random matrix theory, decentralized stochastic approximation, and mean field games. Only recently have those tools started to improve to encompass broader ranges of system models, allowing one to obtain relevant results in realistic scenarios. The target of our research project is to develop these tools in order to address broad problems of complex systems and to encompass them in an original unified theoretical framework.This project represents an opportunity to develop common methodologies for many engineering communities sharing similar challenges in large dimensional stochastic networks, within a new world leading group on mathematical foundations for complex networks."