The restart of the Large Hadron Collider (LHC) at CERN, foreseen in November 2009 after the incident of 2008, will finally open a new window on the physics at the TeV scale and will allow the discovery of the Standard Model Higgs boson, if it exists, or of possible alternative schemes for the spontaneous symmetry-breaking mechanism. Moreover the LHC Collider will hopefully provide an answer to one of the most compelling questions of today coming from astronomical observations, astrophysics and cosmic ray experiments: which is the particle physics candidate for the Dark Matter component of the Universe? Supersymmetry (SUSY) is a theoretically attractive scenario for physics beyond the Standard Model which can provide a suitable Dark Matter c...