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 sqrt(sNN) = 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 pT 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 pT hadrons which yield “tomographic” information of the hottest anddensest phases of the reaction.