QCD analysis and measurement of $W$ boson production in association with jets at the ATLAS detector

The Standard Model of particle physics stands as one of the triumphs of the 20\th{} and 21\st{} century so far. Colliders around the world have been built for the purpose of pushing this theory to its limit, and have consistently found their measurements to be well described. Yet outside of colliders, there is strong evidence that the Standard Model does not completely describe the universe in which we reside. This provides the motivation to continue to push even further, with the hope of resolving these gaping inconsistencies. At this time, many measurements are no longer limited by the power or experimental precision of our colliders -- it is our limited ability to calculate predictions from the Standard Model which is holding us back. To combat this, great effort is being undertaken to measure processes which will help us to calibrate and better understand the finer details of the theory. The production of a $W$ boson in association with jets in proton-proton collisions serves as a precision test of perturbative quantum chromodynamics, and provides access to the composition of the proton. In this thesis, a measurement of this process using the ATLAS detector at the LHC for proton-proton collisions at a centre-of-mass energy of $\sqrt{s} = 13~\TeV$ and integrated luminosity of $36.1~\ifb$ is presented. Results are split by the charge of the $W$ boson and shown for jet multiplicities up to five in comparison with calculations to next-to-leading order in quantum chromodynamics scaled to the next-to-next-to-leading order cross-section. In addition, the results of a similar measurement at a centre-of-mass energy of $\sqrt{s} = 8~\TeV$ have been used for the first time in an analysis of the structure of the proton, giving a significantly improved determination of the sea-quark densities at medium-to-high Bjorken $x$ compared to other fits of ATLAS data.