The WZ production cross section is measured in proton-proton collisions at a centre-of-mass energy √s = 13TeV using data collected with the CMS detector, corresponding to an integrated luminosity of 35.9 fb^-1 . The inclusive cross section is measured to be σ_tot (pp → WZ) = 48.09^+1.00_-0.96(stat)^+0.44_-0.37(theo)^+2.39_-2.17(syst) ± 1.39(lum) pb, resulting in a total uncertainty of -2.78/+2.98 pb. Fiducial cross section and ratios of charge-dependent cross section measurements are provided. Differential cross section measurements are also presented with respect to three variables: the Z boson transverse momentum p_T , the leading jet p_T , and the M(WZ) variable, defined as the invariant mass of the system composed of the three leptons and the missing transverse momentum. Differential measurements with respect to the W boson p_T , separated by charge, are also shown. Results are consistent with standard model predictions, favouring next-to-next-to-leading-order predictions over those at next-to-leading order. Constraints on anomalous triple gauge couplings are derived via a binned maximum likelihood fit to the M(WZ) variable.