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This thesis presents a measurement of the unpolarised, transverse-momentumdependent (TMD) parton distribution function (PDF) fg1 using a J/ψ+γ‚ final state with the ATLAS detector at the Large Hadron Collider (LHC). 2:6 fb−1 of data from proton-proton collisions collected during 2015 as a part of LHC Run 2 is used. The final state of a J/ψ meson produced in association with an isolated photon, initiated from gluon-gluon fusion, is used to give insight into the internal transverse dynamics of the proton. The transverse momentum distribution of the J/ψ+γ ‚ system is reflective of the transverse momentum of the colliding gluons. By measuring the distribution of the gluon transverse momentum and combining this with a model of the gluon distribution in the proton and a collinear PDF, a full description of a TMD is possible. A series of techniques were utilised to extract this gluon transverse momentum distribution, including statistical tools such as boosted decision trees and binned template profile likelihood fits. The mean transverse momentum of the gluons in a Gaussian parameterisation was found to be ⟨k2T⟩ 12 = 1:61 ± 0:28 GeV.