CERN-LHC. The production of $W^{\pm}Z$ events in proton--proton collisions at a centre-of-mass energy of 13 TeV is measured with the ATLAS detector at the LHC. The collected data correspond to an integrated luminosity of 3.2 fb$^{-1}$. The $W^{\pm}Z$ candidates are reconstructed using leptonic decays of the gauge bosons into electrons or muons. The measured inclusive cross section in the detector fiducial region for leptonic decay modes is $\sigma_{W^\pm Z \rightarrow \ell^{'} \nu \ell \ell}^{\textrm{fid.}} = 63.2 \pm 3.2$ (stat.) $\pm 2.6$ (sys.) $\pm 1.5$ (lumi.) fb. In comparison, the next-to-leading-order Standard Model prediction is $53.4^{+3.6}_{-2.8}$ fb. The extrapolation of the measurement from the fiducial to the total phase space yields $\sigma_{W^{\pm}Z}^{\textrm{tot.}} = 50.6 \pm 2.6$ (stat.) $\pm 2.0$ (sys.) $\pm 0.9$ (th.) $\pm 1.2$ (lumi.) pb, in agreement with a recent next-to-next-to-leading-order calculation of $48.2^{+1.1}_{-1.0}$ pb. The cross section as a function of jet multiplicity is also measured, together with the charge-dependent $W^+Z$ and $W^-Z$ cross sections and their ratio. The cross sections are measured in a fiducial phase space reflecting the detector acceptance, defined by: - $p_{\mathrm{T}}$ of electrons and muons from Z0 decays > 15 GeV - $p_{\mathrm{T}}$ of electrons and muons from the $W^{\pm}$ decays > 20 GeV - $|\eta|$ of muons and electrons < 2.5 - Leptons from the Z0 boson are separated by $\Delta R(\ell,\ell) > 0.2$ from each other - Leptons from the Z0 and W bosons are separated by $\Delta R(\ell,\ell) > 0.3$ from each other - |dilepton mass - Z0 mass| < 10 GeV - $m_{\mathrm{T}}$ of $W^{\pm}$ > 30 GeV. At particle level, the kinematics of final-state prompt electrons and muons is computed including the contributions from final-state radiated photons within a distance in the ($\eta,\phi$) plane of $\Delta R = \sqrt{(\Delta\eta)^2 + (\Delta\phi)^2} = 0.1$ around the direction of the charged lepton. These dressed leptons and the final-state neutrinos that do not originate from hadron or $\tau$ decays are associated with the $W$ and $Z$ boson decay products with an algorithmic approach, called ``resonant shape''. This algorithm is based on the value of an estimator expressing the product of the nominal line shapes of the $W$ and $Z$ resonances $P = \left| \frac{1}{ m^2_{(\ell^+,\ell^-)} - \left(m_Z^{\textrm{PDG}}\right)^2 + i \; \Gamma_Z^{\textrm{PDG}} \; m_Z^{\textrm{PDG}} } \right|^2 \times \; \left| \frac {1} { m^2_{(\ell',\nu_{\ell'})} - \left(m_W^{\textrm{PDG}}\right)^2 + i \; \Gamma_W^{\textrm{PDG}} \; m_W^{\textrm{PDG}} } \right|^2$ where $m_Z^{\textrm{PDG}}$ ($m_W^{\textrm{PDG}}$) and $\Gamma_Z^{\textrm{PDG}}$ ($\Gamma_W^{\textrm{PDG}}$) are the world average mass and total width of the $Z$ ($W$) boson, respectively, as reported by the Particle Data Group. The input to the estimator is the invariant mass $m$ of all possible pairs ($\ell^+,\ell^-$) and ($\ell',\nu_{\ell'}$) satisfying the fiducial selection requirements. The final choice of which leptons are assigned to the $W$ or $Z$ bosons corresponds to the configuration exhibiting the highest value of the estimator. The inclusive cross section is also extrapolated to the total phase space and all W and Z boson decay modes. The total phase space is defined by requiring the invariant mass of the lepton pair associated with the Z boson decay to be in the range $66<m_{\ell\ell}<116$ GeV. This result is model-dependent and includes phase space that was not experimentally accessible, so it should be used with caution. Whenever possible, the fiducial cross sections should be used instead, since they are only minimally model-dependent.