  Measurements of $ZZ$ production in the $\ell^{+}\ell^{-}\ell^{\prime
+}\ell^{\prime -}$ channel in proton-proton collisions at 13 TeV center-of-mass
energy at the Large Hadron Collider are presented. The data correspond to 36.1
$\mathrm{fb}^{-1}$ of collisions collected by the ATLAS experiment in 2015 and
2016. Here $\ell$ and $\ell'$ stand for electrons or muons. Integrated and
differential $ZZ \to \ell^{+}\ell^{-}\ell^{\prime +}\ell^{\prime -}$ cross
sections with $Z \to \ell^+\ell^-$ candidate masses in the range of 66 GeV to
116 GeV are measured in a fiducial phase space corresponding to the detector
acceptance and corrected for detector effects. The differential cross sections
are presented in bins of twenty observables, including several that describe
the jet activity. The integrated cross section is also extrapolated to a total
phase space and to all Standard-Model decays of $Z$ bosons with mass between 66
GeV and 116 GeV, resulting in a value of $17.3 \pm 0.9$ [$\pm 0.6$ (stat.) $\pm
0.5$ (syst.) $\pm 0.6$ (lumi.)] pb. The measurements are found to be in good
agreement with the Standard-Model predictions. A search for neutral triple
gauge couplings is performed using the transverse momentum distribution of the
leading $Z$-boson candidate. No evidence for such couplings is found and
exclusion limits are set on their parameters.
