The objective is to enable the simulation of electron and nuclear dynamics of complex materials, liquids and molecular crystals via ab-initio methods based on an open-system formulation of Density Functional Theory (DFT). For complex materials, we focus on layered systems of interest in catalysis and photovoltaics, such as metal dichalcogenides deposited on metal oxide surfaces. Applications to liquids and molecular crystals aim at exploring cooperative effects in the intrinsically non-Markovian dynamics that accompanies an electronic process, such as interactions with a light source, or transport of energy and charge. Electron-nuclear dynamics based on the proposed electronic structure method will be developed at the Ehrenfest level as well as Surface Hopping on a diabatic all-electron basis set generated on-the-fly and applied to charge and energy transfer processes in the condensed phase. The investigations will lead to the first comprehensive fundamental understanding of complex non-Markovian dynamical interactions between the components of composite materials, such as the ability of one component of the system to change the physicochemical behavior of another component. The scientific broader impacts will occur on two fronts: (1) the ab-initio computation of dynamics of complex materials, liquids and molecular crystals will reach longer timescales than ever before due to the intrinsic reduced computational complexity that arises when density embedding is employed; and (2) because the proposed method allows one to dissect molecular properties into intra-subsystem and inter-subsystem, cooperative effects in the dynamical response of these systems will be evaluated and assessed. Particularly important is the case of layered composite materials, for which the interaction between the components can be determinant in the function of the entire material.