Quarkonium studies in p+p and Pb+Pb collisions with CMS

The collisions of Pb nuclei at the LHC will create strongly interacting matter at unprecedented energy densities, allowing us to probe QCD at extreme temperatures and very low parton momentum fractions. This paper presents the capabilities of the CMS experiment to study the production of quarkonium states in $p+p$ and Pb+Pb collisions. The very good acceptance and excellent dimuon mass resolution will allow us to do with the three $\Upsilon$ states (1S, 2S, 3S) the exciting measurements previously performed with the $J/\psi$ and $\psi'$ states, at the SPS and RHIC