This paper is dedicated to the memory of Professor Guido Altarelli who sadly passed away as it went to press. The results which it presents are founded on the principles and the formalism which he developed in his pioneering theoretical work on Quantum Chromodynamics in deep-inelastic lepton-nucleon scattering nearly four decades ago rent e ± p scattering for zero beam polarisation. The data were taken at proton beam energies of 920, 820, 575 and 460 GeV and an electron beam energy of 27.5 GeV. The data correspond to an integrated luminosity of about 1 fb −1 and span six orders of magnitude in negative four-momentum-transfer squared, Q 2 , and Bjorken x. The correlations of the systematic uncertainties were evaluated and taken into account for the combination. The combined cross sections were input to QCD analyses at leading order, next-to-leading order and at next-to-next-to-leading order, providing a new set of parton distribution functions, called HERAPDF2.0. In addition to the experimental uncertainties, model and parameterisation uncertainties were assessed for these parton distribution functions. Variants of HERAPDF2.0 with an alternative gluon parameterisation, HERAPDF2.0AG, and using fixedflavour-number schemes, HERAPDF2.0FF, are presented. The analysis was extended by including HERA data on charm and jet production, resulting in the variant HERAPDF2.0Jets. The inclusion of jet-production cross sections made a simultaneous determination of these parton distributions and the strong coupling constant possible, resulting in α s (M 2 Z ) = 0.1183 ± 0.0009(exp) ± 0.0005(model/parameterisation) ± 0.0012(hadronisation) and results on electroweak unification and scaling violations are also presented. H1 and ZEUS

A combination is presented of the inclusive deep inelastic cross sections measured by the H1 and ZEUS Collaborations in neutral and charged current unpolarised e ± p scattering at HERA during the period 1994-2000. The data span six orders of magnitude in negative four-momentum-transfer squared, Q 2 , and in Bjorken x. The combination method used takes the correlations of systematic uncertainties into account, resulting in an improved accuracy. The combined data are the sole input in a NLO QCD analysis which determines a new set of parton distributions, HERAPDF1.0, with small experimental uncertainties. This set includes an estimate of the model and parametrisation uncertainties of the fit result.

Next-to-leading-order QCD analyses of the ZEUS data on deep inelastic scattering together with fixed-target data have been performed, from which the gluon and quark densities of the proton and the value of the strong coupling constant ␣ s (M Z ) were extracted. The study includes a full treatment of the experimental systematic uncertainties including point-to-point correlations. The resulting uncertainties in the parton density functions are presented. A combined fit for ␣ s (M Z ) and the gluon and quark densities yields a value for ␣ s (M Z ) in agreement with the world average. The parton density functions derived from ZEUS data alone indicate the importance of HERA data in determining the sea quark and gluon distributions at low x. The limits of applicability of the theoretical formalism have been explored by comparing the fit predictions to ZEUS data at very low Q 2 .