  We present the first unbiased determination of parton distribution functions
(PDFs) with electroweak corrections. The aim of this thesis is to provide an
exhaustive description of the theoretical framework and the technical
implementation which leads to the determination of a set of PDFs which includes
the photon PDF and quantum electrodynamics (QED) contributions to parton
evolution. First, we introduce and motivate the need of including electroweak
corrections to PDFs, providing phenomenological examples and presenting an
overview of the current state of the art in PDF fits. The theoretical
implications of such corrections are then described through the implementation
of the combined QCD+QED evolution in APFEL, a public code for the solution of
the PDF evolution developed particularly for this thesis. We proceed by
presenting the new structure of the Neural-Network PDF (NNPDF) methodology used
for the extraction of this set of PDFs with QED corrections. We then provide a
first determination of the full set of PDFs based on deep-inelastic scattering
data and LHC data for $W$ and $Z/\gamma^*$ Drell-Yan production, using
leading-order QED and NLO or NNLO QCD: the so-called NNPDF2.3QED set of PDFs.
We perform a preliminary investigation of the phenomenological implications of
NNPDF2.3QED set, in particular, focusing on the photon-induced corrections to
direct photon production at HERA, high-mass dilepton and $W$ pair production at
the LHC and finally, providing a first determination of lepton PDFs through the
APFEL evolution. We conclude with a summary of the technological upgrades
required for the improvement of future PDF determinations with electroweak
corrections.
