Measurements of the associated production of a top quark pair and a $Z$ boson with the ATLAS detector

This thesis presents measurements of the inclusive and differential cross-sections of a top quark pair produced in association with a $Z$ boson with the ATLAS detector. The full LHC Run-2 dataset corresponding to an integrated luminosity of $139 \, \text{fb}^{-1}$ collected during proton-proton collisions at a centre-of-mass energy of $13 \, \text{TeV}$ is used in the measurements. The thesis focuses on the three-lepton final states of the $t\bar{t}Z$ system where only electrons or muons are considered. The measured inclusive cross-section is $\sigma(pp \rightarrow t\bar{t}Z = 0.99 \pm 0.05 \, \text{(stat.)} \pm 0.08 \, \text{(syst.)} \, \text{pb} = 0.99 \pm 0.10 \, \text{pb}$. It is in good agreement with other experimental observations and the theoretical prediction of $\sigma_{t\bar{t}Z} = 0.86^{+0.07}_{-0.08} \, \text{(scale)} \pm 0.02 \, \text{(PDF)} \, \text{pb}$. The measurements of the differential cross-sections are performed using profile likelihood unfolding. A comprehensive set of eight observables is used to probe different aspects of the $t\bar{t}Z$ production. The differential cross-section in each observable is measured to be in good agreement with the theoretical prediction which uses the Madgraph5_aMC@NLO+Pythia8 Monte Carlo event generation. The measurements presented in this thesis achieve a significant improvement in precision with respect to the previous ATLAS measurements.