The baseline of GAIA is the study of the formation and evolution of the Milky Way from astrometric and photometric measurements. The mission displays a remarkable versatility in its applications, including a significant impact in fundamental physics. In the following I will try to define the relationship between astrometry and fundamental physics, before considering in more detail the determination of the space curvature and the study of the non linearity of gravity from the astrometric measurements. It is shown that GAIA is perfectly at home to sense the bending of light-rays in the solar gravitational field and should be able to determine the PPN parameter γ with a precision between 10-6 and 10-7, much better than any other determination expected by 2015. A favorable combination of distances and eccentricities on a handful of minor planets will permit to search for the relativistic perihelion precession. The parameter β should be ascertained to 10-3-10-4 provided the solar quadrupole moment is not solved simultaneously and constrained from other sources. This achievable accuracy rests also on assumptions regarding the reconstruction of orbits of minor planets from GAIA-only observations.