This report presents the capabilities of the 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 √ s N N = 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 report covers 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 T inclusive hadron identified spectra and elliptic flow) which provide information on the collective properties of the system, as well as perturbative probes such as quarkonia, heavy-quarks, jets and high p T hadrons which yield "tomographic" information of the hottest and densest phases of the reaction.