"Frontier research in statistical mechanics and soft condensed matter focuses on systems of ever-increasing complexity. Among these are systems where microscopic dynamics are not controlled by thermal fluctuations, either because the sources of the fluctuations have not a thermal origin, or because “microscopic” sources of fluctuations are altogether absent. Practical applications comprise everyday products such as paints or foodstuff which are soft solids composed of dense suspensions of particles that are too large for thermal fluctuations to play any role. Non-Brownian “active” matter, obtained when particles internally produce motion, represents another growing field with applications in biophysics and soft matter. Because these systems all evolve far from equilibrium, there exists no general framework to tackle these problems theoretically from a fundamental perspective. I will develop a radically new approach to lay the foundations of a detailed theoretical understanding of the physics of a broad but coherent class of materials evolving far from equilibrium. To go beyond phenomenology, I will carry theoretical research to elucidate the physics of particle systems that are simultaneously Dense, Disordered, Driven and Dissipative—D4PARTICLES. By combining numerical analysis of model systems to fully microscopic statistical mechanics analysis, my overall aim is to discover the general principles governing the physics of athermal particle systems far from equilibrium and to reach a complete theoretical understanding and obtain predictive tools regarding the phase behavior, structure and dynamics of D4PARTICLES. Reaching a new level of theoretical understanding of a broad range of materials will impact fundamental research by opening up statistical physics to a whole new class of complex systems and should foster experimental activity towards design and quantitative characterization of large class of disordered solids and soft materials."