  This paper presents measurements of $W^{\pm}Z$ production cross sections in
$pp$ collisions at a centre-of-mass energy of 13 TeV. The data were collected
in 2015 and 2016 by the ATLAS experiment at the Large Hadron Collider, and
correspond to an integrated luminosity of 36.1 fb$^{-1}$. The $W^{\pm}Z$
candidate events are reconstructed using leptonic decay modes of the gauge
bosons into electrons and muons. The measured inclusive cross section in the
detector fiducial region for a single leptonic decay mode is $\sigma_{W^\pm Z
\rightarrow \ell^{'} \nu \ell \ell}^{\textrm{fid.}} = 63.7 \pm 1.0$ (stat.)
$\pm 2.3$ (syst.) $\pm 1.4$ (lumi.) fb, reproduced by the
next-to-next-to-leading-order Standard Model prediction of $61.5^{+1.4}_{-1.3}$
fb. Cross sections for $W^+Z$ and $W^-Z$ production and their ratio are
presented as well as differential cross sections for several kinematic
observables. An analysis of angular distributions of leptons from decays of $W$
and $Z$ bosons is performed for the first time in pair-produced events in
hadronic collisions, and integrated helicity fractions in the detector fiducial
region are measured for the $W$ and $Z$ bosons separately. Of particular
interest, the longitudinal helicity fraction of pair-produced vector bosons is
also measured.
