The baseline of GAIA is the study of the formation and evolution ofthe Milky Way from astrometric and photometric measurements. Themission displays a remarkable versatility in its applications,including a significant impact in fundamental physics. In thefollowing I will try to define the relationship between astrometry andfundamental physics, before considering in more detail thedetermination of the space curvature and the study of the nonlinearity of gravity from the astrometric measurements. It is shownthat GAIA is perfectly at home to sense the bending of light-rays inthe solar gravitational field and should be able to determine the PPNparameter γ with a precision between 10-6 and 10-7,much better than any other determination expected by 2015. Afavorable combination of distances and eccentricities on a handful ofminor planets will permit to search for the relativistic perihelionprecession. The parameter β should be ascertained to 10-3-10-4 provided the solar quadrupole moment is not solvedsimultaneously and constrained from other sources. This achievableaccuracy rests also on assumptions regarding the reconstruction oforbits of minor planets from GAIA-only observations.