With the recent discovery of a Higgs-like particle at the Large Hadron Collider (LHC), particle physics has entered a completely new era. The central goal for high energy physics in the following years will be the detailed determination of the properties of this new particle, in particular checking its consistency with the Standard Model Higgs boson hypothesis, and to further explore the highest energy domain in search for further new physics, like supersymmetry or extra dimensions, closely related to the Higgs-like boson properties and to dark matter and dark energy studies. It is thus of paramount importance to be able to provide accurate theoretical predictions for signal and background processes both for Higgs production and for hypothetical new particles, in order to optimize both the characterization of cross sections, couplings and branching fractions, but also to maxime the LHC discovery potential. A crucial ingredient of these theoretical predictions for an hadron collider as the LHC are the Parton Distribution Functions (PDFs) of the proton. This project aims to fully exploit the LHC potential to achieve the ultimate experimental and theoretical precision in the determination of PDFs to make essential contributions to our understanding of the structure of the nucleon, in particular in the regions more relevant for Higgs and BSM physics searches at the LH, the match between PDFs and NLO Monte Carlo event generators, a crucial tool for accurate exclusive event description at the LHC, and to propose new avenues in New Physics searches from precision LHC measurements, where PDFs are often the dominant systematic uncertainties.