LHCb is an heavy flavour precision experiment with LHC at CERN. It will search for New Physics in CP violation and rare decays in the heavy quarks sector. The experiment is ready to take data for the soon expected start-up of the LHC. An overview of its physics program in both the rare decays of B hadrons and CP violation in the charm sectors is given, illustrated by few key examples: measurements of the \bstomumu\ and \btokstmumu\ decay modes, study of the photon helicity using the \bstophig\ and \btokstee\ decay modes, as well as search for CP violation using D^0 mesons