Parton Distribution Functions are sets of functions that provide the momenta distributions of the constituent particles within a hadron, typically the proton, at different energy scales. This thesis describes the inclusion of Quantum Electrodynamics (QED) corrections to the existing set of MMHT (Martin, Motylinski, Harland-Lang, Thorne) Parton Distribution Functions (PDFs) which contains the photon PDF of the proton. Adopting an input distribution from the LUXqed formulation, a consistency is found with other recent sets and the methods of including QED effects for the full, coupled Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution of all partons with QED at O(α), O(ααS ), O(α^2) are discussed. Building on this, a set of QED corrected neutron PDFs are presented and the photon PDF provided, separated into its elastic and inelastic contributions. The resultant effects of QED on the other partons are investigated, as well as the effects of the evolution on the fit quality of the PDFs, whilst outlining the sources of uncertainty for the photon. Finally the phenomenological implications of this set are explored, giving the partonic luminosities for both the elastic and inelastic photon interactions and the effect of our photon PDF on fits to high mass Drell-Yan measurements with the inclusion of photon initiated processes
