GIARPS (GIAno and haRPS) is a project devoted to have on the same focal station of the Telescopio Nazionale Galileo (TNG) both the high resolution spectrographs HARPS-N (VIS) and GIANO (NIR) working simultaneously. This could be considered the first and unique worldwide instrument providing cross-dispersed echelle spectroscopy at a high resolution (R=115,000 in the visual and R=50,000 in the IR) and over in a wide spectral range (0.383 - 2.45 μm) in a single exposure. The science case is very broad, given the versatility of such an instrument and the large wavelength range. A number of outstanding science cases encompassing mainly extra-solar planet science starting from rocky planet search and hot Jupiters, atmosphere characterization can be considered. Furthermore both instrument can measure high precision radial velocity by means the simultaneous thorium technique (HARPS - N) and absorbing cell technique (GIANO) in a single exposure. Other science cases are also possible. Young stars and proto- planetary disks, cool stars and stellar populations, moving minor bodies in the solar system, bursting young stellar objects, cataclysmic variables and X-ray binary transients in our Galaxy, supernovae up to gamma-ray bursts in the very distant and young Universe, can take advantage of the unicity of this facility both in terms of contemporaneous wide wavelength range and high resolution spectroscopy.