The production of Z boson pairs in proton–proton (pp) collisions, pp→(Z/γ∗)(Z/γ∗)→2ℓ2ℓ′, where ℓ,ℓ′=e or μ, is studied at a center-of-mass energy of 13TeV with the CMS detector at the CERN LHC. The data sample corresponds to an integrated luminosity of 137fb−1, collected during 2016–2018. The ZZ production cross section, σtot(pp→ZZ)=17.4±0.3(stat)±0.5(syst)±0.4(theo)±0.3(lumi) pb, measured for events with two pairs of opposite-sign, same-flavor leptons produced in the mass region 60<mℓ+ℓ−<120GeV is consistent with standard model predictions. Differential cross sections are also measured and agree with theoretical predictions. The invariant mass distribution of the four-lepton system is used to set limits on anomalous ZZZ and ZZγ couplings.