The NNPDF3.0 set of parton distribution functions (PDFs) is presented, representing the first set of PDFs determined using a methodology validated by a closure test. This methodology ensures that procedural uncertainties are negligible compared to theoretical and experimental uncertainties. The closure test involves generating artificial data from a known underlying law and fitting PDFs to these data, demonstrating that the fitted PDFs correctly reproduce the statistical distributions expected based on the assumed experimental uncertainties. The NNPDF3.0 set includes a wide range of experimental data, such as HERA-II deep-inelastic scattering, jet production from ATLAS and CMS, vector boson rapidity and transverse momentum distributions, $W+c$ data from CMS, and top quark pair production cross sections from ATLAS and CMS. The PDFs are provided at leading order (LO), next-to-leading order (NLO), and next-to-next-to-leading order (NNLO) in perturbative QCD, with electroweak corrections included. The dataset covers a variety of kinematic ranges and experimental uncertainties, and the methodology has been improved to ensure independence of procedural uncertainties. The implications of the NNPDF3.0 set for LHC phenomenology, particularly for Higgs production in gluon fusion, are discussed.The NNPDF3.0 set of parton distribution functions (PDFs) is presented, representing the first set of PDFs determined using a methodology validated by a closure test. This methodology ensures that procedural uncertainties are negligible compared to theoretical and experimental uncertainties. The closure test involves generating artificial data from a known underlying law and fitting PDFs to these data, demonstrating that the fitted PDFs correctly reproduce the statistical distributions expected based on the assumed experimental uncertainties. The NNPDF3.0 set includes a wide range of experimental data, such as HERA-II deep-inelastic scattering, jet production from ATLAS and CMS, vector boson rapidity and transverse momentum distributions, $W+c$ data from CMS, and top quark pair production cross sections from ATLAS and CMS. The PDFs are provided at leading order (LO), next-to-leading order (NLO), and next-to-next-to-leading order (NNLO) in perturbative QCD, with electroweak corrections included. The dataset covers a variety of kinematic ranges and experimental uncertainties, and the methodology has been improved to ensure independence of procedural uncertainties. The implications of the NNPDF3.0 set for LHC phenomenology, particularly for Higgs production in gluon fusion, are discussed.