Measurements of ZZ production in the l(+)l(-)l'(+)l'(-) 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 fb(-1) of collisions collected by the ATLAS experiment in 2015 and 2016. Here l and l ' stand for electrons or muons. Integrated and differential ZZ -> l(+)l(-)l'(+)l'(-) cross sections with Z -> l(+)l(-) 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 +/- 0.9 [+/- 0.6(start) +/- 0.5 (syst) +/- 0.6 (lumi)] pb. The measurements are found to be in good agreement with the standard model. 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.