CERN-LHC. An observation of electroweak $W^{\pm}Z$ production in association with two jets in proton-proton collisions is presented. The data collected by the ATLAS detector at the Large Hadron Collider in 2015 and 2016 at a centre-of-energy of $\sqrt{s}$ = 13TeV are used, corresponding to an integrated luminosity of 36.1 $fb^{-1}$. Events containing three identified leptons, either electrons or muons, and two jets are selected. The electroweak production of $W^{\pm}Z$ bosons in association with two jets is measured with an observed significance of 5.3 standard deviations. A fiducial cross section for electroweak production including interference effects is measured to be $\sigma_{WZjj-EW}$ = 0.57^{+0.14}_{-0.13} (stat.) ^{+0.07}_{-0.06} (syst.) fb. Differential cross section of $W^{\pm}Zjj$ production for several kinematic observables are also measured. Fiducial phase space definition for the measurement: - $p_{\mathrm{T}}$ 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 least 2 jets with opposite $|\eta|$. Jets are particle level jets with anti-kt R=0.4. - $p_{\mathrm{T}}$ of the two jets > 40 GeV - $|\eta|$ of the two jets < 4.5 - the first jet is chosen as the leading $p_{\mathrm{T}}$ jet - the second jet is chosen among the remaining jets as the jet of highest $p_{\mathrm{T}}$ with $|\eta|$ opposite to the first jets - invariant mass of the two jets > 500 GeV - leptons and jets separated by $\Delta R(\ell,jet) > 0.3$ - processes with a b-quark in the initial state are excluded 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 \cite{Agashe:2014kda}. 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 defined in the next paragraph. 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.