High Energy Physics at Low(er) Energies: Precision Measurements in Top Quark Physics at $\sqrt{s} = 5.02$ TeV

The top quark is the heaviest of all known subatomic particles with a mass similar to that of a tungsten atom. Furthermore, it has the shortest lifetime of all quarks and is the only one that can be studied as a ``free'' quark. With the discovery of the Higgs boson at the Large Hadron Collider (LHC) in 2012 and no sign of any physics beyond the Standard Model (SM), measurements of the top quark provide an alternate approach to understanding and testing the SM. This thesis will present two measurements of the top quark at a centre-of-mass energy of 5.02 TeV with 257 $\text{pb}^{-1}$ of proton-proton collision data collected by the ATLAS detector. The first is a $t\bar{t}$ cross-section measurement that is used to constrain the gluon Parton Distribution Function (PDF) at high Bjorken $x$ and the second is a search for $t$-channel single-top-quark production. The pair production cross-section was measured individually in both the dilepton and single-lepton channels of the $t\bar{t}$ decay before being combined. The measurement in the single-lepton channel is currently the most precise measurement of the top-quark pair production cross-section by the ATLAS Collaboration to date. The $t$-channel cross-section is measured in the semi-leptonic decay of the top quark and is the first observation of this process at $\sqrt{s} = 5.02$ TeV.