The primary goal of this research proposal is to push to new levels of precision the predictive power of theoretical analyses of the phenomena observed at the Large Hadron Collider (LHC) at CERN. The start-up of the LHC has opened a new era in the exploration of the fundamental laws of Nature. This is expected to lead, among other results, to the clarification of the mechanism breaking the electroweak symmetry of fundamental interactions, to the discovery of new elementary particles, possibly accounting for the Dark Matter seen in the cosmos, and to the observation of new interactions, acting differently on matter and antimatter, to explain the observed baryon asymmetry of the universe.The crucial ingredient in the success of this ambitious programme is the ability to interpret the signals extracted by the experiments. To decode their properties and match them to the dynamics of possible new physics models relies on the numerical simulation of such dynamics, and on the ability to distinguish it from that of the known Standard Model (SM) processes. The past two decades have witnessed a continuous progress in this field, driven by the exploitation of the data from previous colliders, such as LEP, HERA and the Tevatron. The complexity of the LHC final states, the large rates of processes with many jets and their role in mimicking the production and decay of possible new particles, call for an aggressive effort to radically improve the current quality and accuracy of the theoretical modelling, to match the unprecedented discovery potential and measurement precision of the LHC experiments.Capitalizing on recent theoretical advances, driven in significant part by the work of the PI and the team members, this proposal outlines a challenging and ambitious programme to advance to new levels the precision, generality and scope of the analysis tools used by both experimentalists and theorists engaged in LHC physics.