Jet Production at Low and High $Q^2$ and Determination of the Strong Coupling ${\alpha }_s$ at H1

Two recent measurements of inclusive jet, 2-jet and 3-jet cross sections in deep-inelastic $ep$ scattering from the H1 collaboration are presented. The measurements are performed at low $5<Q^2<100$ GeV${}^2$ and high $150<Q^2<15000$ GeV${}^2$ virtualities of the exchanged boson. The obtained cross sections are in good agreement with perturbative QCD calculations at NLO and are used to extract the strong coupling ${\alpha }_s(M_Z)$. The experimental precision is 0.6% and 1.2% for the high and low $Q^2$ regimes, respectively. The error on the obtained value of ${\alpha }_s(M_Z)$ is dominated by the theoretical uncertainties which are mostly due to missing higher orders. At low $Q^2$ the uncertainty due to terms beyond NLO amounts to 7.5%. The determination of ${\alpha }_s$ at various scales shows the running of the strong coupling over a large range.