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This document collects a written summary of all contributions presented atthe workshop "$\alpha_s$(2019): Precision measurements of the strong coupling"held at ECT* (Trento) in Feb. 11--15, 2019. The workshop explored in depth thelatest developments on the determination of the QCD coupling $\alpha_s$ fromthe key categories where high precision measurements are available: (i) latticeQCD, (ii) hadronic $\tau$ decays, (iii) deep-inelastic scattering and partondistribution functions, (iv) event shapes, jet cross sections, and otherhadronic final-states in $e^+e^-$ collisions, (v) Z boson and W boson hadronicdecays, and (vi) hadronic final states in p-p collisions. The status of thecurrent theoretical and experimental uncertainties associated to eachextraction method, and future perspectives were thoroughly reviewed. Novel$\alpha_s$ determination approaches were discussed, as well as the combinationmethod used to obtain a world-average value of the QCD coupling at the Z masspole.

$\alpha_s$(2019): Precision measurements of the QCD coupling