"We have entered the fascinating era of the Large Hadron Collider (LHC).Both the searches for new physics in proton-proton collisions andthe investigations of the high-energy medium effects in heavy-ion (HI) collisions require a solid understanding of multiplegluonic interactions. With an increase in energy, gluon densities rise rapidly.When probed at very high energies, heavy nuclei and even protonsappear as dense gluonic clouds.The main objective of this proposal is to further develop the theory of high-energy collisions of dense objectsfrom first-principle calculations and to apply it to phenomenology at the LHC and at the proposedElectron-Ion and Large Hadron-electron Colliders. We focus on collisions involving HIs, wherethe effects of high densities become enhanced not only by energy but alsoby the number of nucleons in the nuclei.Our specific goals are:A: The derivation of an effective QCD-based theory forthe initial phase of HI collisions.B: The achievement of a systematicphenomenological description of a certain class of measurements that are of particular importancefor the HI program at the LHC.C: The theoretical support for future electon-hadron experiments.The objectives of this proposal will be achievedvia strengthening and broadening of a long-lasting collaboration between research centers from EU and the US aiming at the development of a unified,QCD-based theoretical framework to describe the structure and collisions of hadrons and nuclei.The results of this study will facilitate a better understanding of a quantum field theory, such as QCD, beyond naive perturbationtheory. Today, exploring QCD under extreme conditions, such as at high energy/density,is more important than ever due to its relevance for the LHC and future collider programs.In this project we address questions fundamental to understanding the experimental results."