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 fb−1 collected during proton-proton collisions at a centre-of-mass energy of √ s =13 TeV is used in the measurements. The thesis focuses on the three-lepton final states of the t ¯tZ system where only electrons or muons are considered. The measured inclusive cross-section is σ(pp → t ¯tZ) = 0.99 ± 0.05 (stat.) ± 0.08 (syst.) pb = 0.99 ± 0.10 pb. It is in good agreement with other experimental observations and the theoretical prediction of σt ¯tZ = 0.86+0.07 −0.08 (scale) ± 0.02 (PDF) 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 ¯tZ 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.