High-density QCD with CMS at the LHC

We will present the capabilities of the Compact Muon Solenoid (CMS) experiment to explore the rich heavy-ion physics programme offered by the CERN Large Hadron Collider (LHC). The collisions of lead nuclei at energies $\sqrt{s_{_{NN}}}$ = 5.5 TeV will probe quark and gluon matter at unprecedented values of energy density. The prime goal of this research is to study the fundamental theory of the strong interaction --- Quantum Chromodynamics (QCD) --- in extreme conditions of temperature, density and parton momentum fraction (low-$x$). This presentation will cover in detail the potential of CMS to carry out a series of representative Pb-Pb measurements. These include ``bulk'' observables --- charged hadron multiplicity, low $p_{\rm T}$ inclusive hadron identified spectra and elliptic flow --- which provide information on the collective properties of the system; as well as perturbative processes --- such as quarkonia, heavy-quarks, jets, $\gamma$-jet, and high $p_{\rm T} $ hadrons --- which yield ``tomographic'' information on the hottest and densest phases of the reaction.