  The inclusive as well as differential cross section of the associated
production of top-antitop quark pairs and a $Z$ boson ($t\bar{t}Z$) is measured
in final states with exactly three or four isolated leptons (electrons or
muons). For this purpose, the full LHC Run 2 dataset of proton-proton
collisions recorded by the ATLAS detector from $2015$ to $2018$, which
corresponds to an integrated luminosity of $139\,\text{fb}^{-1}$, is used. The
inclusive production cross section is measured to be
$\sigma_{t\bar{t}Z}=1.05\pm0.05\,(\text{stat.})\,\pm0.09\,(\text{syst.})\,\text{pb}$,
which is in agreement with the most precise Standard Model theoretical
prediction. Absolute and normalised differential cross section measurements are
performed as a function of various kinematic variables in order to probe the
kinematics of the $t\bar{t}Z$ system within both parton- and particle-level
phase spaces.
