Past, present and future challenges in the determination of the structure of the proton
Since the first Deep Inelastic Scattering experiments at SLAC, the subnuclear structure of the proton has been a key ingredient to verify and test Quantum Chromo Dynamics. In time, a sophisticated theoretical, statistical and experimental framework has been elaborated to parametrise the proton in terms of its elementary constituents, quarks and gluons. Nowadays a robust and detailed knowledge of the proton subnuclear structure is a crucial input at the Large Hadron Collider (LHC). The uncertainty on the Parton Distribution Functions (PDFs) - the functions that parametrise protons in terms of quarks and gluons - often represents a limiting factor in the accuracy of theoretical predictions. At the same time the precise measurements taken at the LHC give a powerful insight on the proton. In the series of lectures I will give a detailed overview of the key theoretical, statistical and experimental aspects behind PDFs determination. I will then give an overview on the state of the art of modern PDF fits. I will then mention the new exciting theoretical and statistical challenges that the precision frontier reached by the LHC is opening up.