Measurements of the jet and vector boson in association with jets production, extraction of $\alpha_s$ and PDF constrains at CMS

We present CMS results related to jet production cross sections, which pose a central test to perturbative QCD predictions. Results include recent jet, dijet, multijet differential cross section and hadronic event shape measurements in pp collisions at a center-of-mass energy of 7 and 8 TeV using datacollected in the CMS experiment.Total and differential cross-section measurements of vector bosons producedin association with jets and heavy flavour quarks are presented.The measurements are compared to next-to leading order calculations and eventsimulations that devise matrix element calculations interfaced with partonshowers. Recent CMS results related to the extraction of the strong coupling constant and PDF are discussed.