The main goal of this project is to develop theoretical and phenomenological tools in the framework of Quantum Chromodynamics (QCD) at high gluon densities oriented to the understanding on data from the Heavy Ion program at the LHC and from the Pierre Auger Observatory on cosmic rays.One main goal of this proposal is to provide a precise characterization of the initial state of heavy ion collisions in order to allow a precise extraction of the transport parameters of the produced medium, presumably a Quark Gluon Plasma. This implies achieving a precise description of the full phase space and collision geometry dependence of the initial quark and gluon distributions and their correlations.The theoretical work of this project focuses in the calculation of higher order corrections to the Color Glass Condensate (CGC) effective theory for QCD high-energy scattering, both at the level of the non-linear evolution equations and of production processes.The theoretical results shall be used to build a Monte Carlo simulation tool for the characterisation of the initial stages of proton and nuclear collisions. The small Bjorken-x component of the nuclear wave function, a key ingredient for the calculation of any production processes studied in this project, shall be constructed under the Gaussian approximation and empirically constrained through global fits to data from several collision systems (e+p, p+p, p+A and A+A).Other objective of this project is to translate the advances in our understanding of high-energy QCD scattering gained by the detailed study of LHC data into the simulation tools used in the analyses of Ultra High Energy Cosmic Rays. This will allow for theoretically well constrained extrapolations over more than two orders of magnitude in the collision energy of several of the hadronic observables of great relevance for the development of the air-showers and, hence, for the interpretation of the experimental results.