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Inclusive jet, dijet and trijet differential cross sections are measured inneutral current deep-inelastic scattering for exchanged boson virtualities 150< Q^2 < 15000 GeV^2 using the H1 detector at HERA. The data were taken in theyears 2003 to 2007 and correspond to an integrated luminosity of 351 pb^{-1}.Double differential Jet cross sections are obtained using a regularisedunfolding procedure. They are presented as a function of Q^2 and the transversemomentum of the jet, P_T^jet, and as a function of Q^2 and the proton'slongitudinal momentum fraction, Xi, carried by the parton participating in thehard interaction. In addition normalised double differential jet cross sectionsare measured as the ratio of the jet cross sections to the inclusive neutralcurrent cross sections in the respective Q^2 bins of the jet measurements.Compared to earlier work, the measurements benefit from an improvedreconstruction and calibration of the hadronic final state. The cross sectionsare compared to perturbative QCD calculations in next-to-leading order and areused to determine the running coupling and the value of the strong couplingconstant as alpha_s(M_Z) = 0.1165 (8)_exp (38)_{pdf,theo}.

Measurement of Multijet Production in ep Collisions at High Q^2 and Determination of the Strong Coupling alpha_s