A measurement of the ZZ production cross section in proton-proton collisions at √ = 7 TeV using data recorded by the ATLAS experiment at the Large Hadron Collider is presented. In a data sample corresponding to an integrated luminosity of 4.6 fb-1 collected in 2011, events are selected that are consistent either with two Z bosons decaying to electrons or muons or with one Z boson decaying to electrons or muons and a second Z boson decaying to neutrinos. The ZZ → ℓ + ℓ - ℓ ′+ ℓ ′- and ZZ → ℓ + ℓ - ℓv̄v cross sections are measured in restricted phase-space regions. These results are then used to derive the total cross section for ZZ events produced with both Z bosons in the mass range 66 to 116 GeV, σZZtot = 6.7 ± 0.7 (stat.) -0.3+0.4 (stat.) ± 0.3 (lumi.) pb, which is consistent with the Standard Model prediction of 5.89-0.18+0.22 pb calculated at next-to-leading order in QCD. The normalized differential cross sections in bins of various kinematic variables are presented. Finally, the differential event yield as a function of the transverse momentum of the leading Z boson is used to set limits on anomalous neutral triple gauge boson couplings in ZZ production. © 2013 Cern for the benefit of the ATLAS collaboration.