Quarkonium production in pp collisions with the CMS detector

The studies of the inclusive production of heavy quarkonium states at LHC are very important to improve our understanding of QCD and hadron formation, given that the heavy-quark masses allow the application of theoretical tools less sensitive to nonperturbative effects. The prompt cross sections and polarizations measured by CMS and the other LHC experiments are presented for the five S-wave states $J/\psi$, $\psi(2S)$ and $\Upsilon(nS)$ ($n=1,2,3$) and discussed especially in comparison to the theoretical predictions provided by Non Relativistic QCD.