Ultra-relativistic heavy-ion collisions are believed to provide the extreme conditions of energy densities able to lead to a transition to a short-lived state, called Quark-Gluon Plasma (QGP), where the quarks are no longer bound inside hadrons. The studies performed so far, formerly at SPS (CERN) and later at RHIC (BNL), allowed to achieve a multitude of crucial results consistent with the hypothesis that a new phase of the QCD matter has been indeed created. However, the emerging picture is that of the formation of a strongly interacting medium with negligibly small viscosity, a perfect liquid, rather than the ideal perturbative QCD parton-gas predicted by most theorists. The head-on collisions between lead nuclei at the unprecedented energies of the forthcoming Large Hadron Collider (LHC) at CERN, due to start in 2008, will allow to measure the properties of compressed and excited nuclear matter at even higher initial densities and temperatures, far above the predicted QCD phase transition point. The longer duration of the quark-gluon plasma phase and the much more abundant production of hard probes, which depend much less on details of the later hadronic phase, will likely provide a consistent and uncontroversial experimental evidence of the QGP formation. Among the signals that witness the change in the nature of the state of nuclear matter, the chemical equilibrium value of the strangeness plays a key role since it is directly sensitive to the matter properties and provides information on the link between the partonic and the hadronic phases. The aim of this course is to overview the underlying goals, the current status and the prospect of the physics of the nucleus-nucleus collisions at ultrarelativistic energies. Among the experimental methods adopted to investigate the challenging signatures of the QGP formation, emphasis on those related to the strangeness flavour will be given.