Four-lepton production in proton-proton collisions, pp→(Z/γ∗)(Z/γ∗)→4ℓ , where ℓ=e or μ , is studied at a center-of-mass energy of 13 TeV with the CMS detector at the LHC. The data sample corresponds to an integrated luminosity of 35.9 fb−1 . The ZZ production cross section, σ(pp→ZZ)=17.2±0.5(stat)±0.7(syst)±0.4(theo)±0.4(lumi) pb , measured using events with two opposite-sign, same-flavor lepton pairs produced in the mass region 60<mℓ+ℓ−<120GeV , is consistent with standard model predictions. Differential cross sections are measured and are well described by the theoretical predictions. The Z boson branching fraction to four leptons is measured to be B(Z→4ℓ)=4.8±0.2(stat)±0.2(syst)±0.1(theo)±0.1(lumi)×10−6 for events with a four-lepton invariant mass in the range 80<m4ℓ<100GeV and a dilepton mass mℓℓ>4GeV for all opposite-sign, same-flavor lepton pairs. The results agree with standard model predictions. The invariant mass distribution of the four-lepton system is used to set limits on anomalous ZZZ and ZZ γ couplings at 95% confidence level: −0.0012<fZ4<0.0010 , −0.0010<fZ5<0.0013 , −0.0012<fγ4<0.0013 , −0.0012<fγ5<0.0013 .