The aim of PLEXMATH is that of formulating a brand new mathematical framework for the analysis of multi-level time-dependent complex networks in terms of tensor-like structures, in particular rank-four objects that represent with four indices the most general structure of possible connections. Generally speaking, our goal is similar to that of Maxwell equations when representing the foundation of classical electromagnetism, i.e. to provide a closed representation of the theory (of complex networks in our case) unifying notation and dynamical equations.We therefore will accommodate current and future theoretical and algorithmic needs by adopting a radically new point of view. Capitalizing on 4th-rank order algebra we will reformulate all network descriptors and will propose dynamical equations to represent diffusive processes on multiplex networks. In doing this, we will generate new mathematical models that will be validated on unparalleled amounts of ICT data that describe relevant socioeconomic and techno- social systems, like the structure and dynamics of social networks and transportation systems that operate at different levels. PLEXMATH constitutes a vital step towards a more general formalism for real-world networks, as the generated knowledge will substantially improve our understanding of complex systems, and will directly impact the way we deal with structural and dynamical patterns in many systems, including ICT.