Using first-principles molecular dynamics, we investigate the interactions of water with the (0001) α-quartz surface. Both the cleaved (unreconstructed) surface, which presents non-bridging oxygen atoms, and the dense surface, which is characterized by 3-membered and 6 membered-rings with siloxane bonds at the top, are considered. The cleaved surface is found to be very hydrophilic. When a water molecule arrives at the surface, its oxygen atom bonds to an under-coordinated Si atom. One of its hydrogen atoms is then transferred to a neighboring non-bridging oxygen through the formation of a hydrogen bond. When the surface is already partially hydrated, the formation of hydrogen-bond chains is observed between the water molecule and adjacent silanol groups. By contrast, the dense surface is shown to be hydrophobic. Our calculations provide qualitative information on the possible reaction paths for the dehydration mechanisms, and more generally on the interactions of water with amorphous SiO2 surfaces.