A bstract The WZ production cross section is measured in proton-proton collisions at a centre-of-mass energy $$ \sqrt{s} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msqrt><mml:mi>s</mml:mi></mml:msqrt></mml:math> = 13 TeV 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 − 0.96 + 1.00 (stat) − 0.37 + 0.44 (theo) − 2.17 + 2.39 (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.