UVMag is a space project currently under R&D study. It consists in a medium-size telescope equipped with a spectropolarimeter to observe in the UV and optical wavelength domains simultaneously. Its first goal is to obtain time series of selected magnetic stars over their rotation period, to study them from their surface to their environment, in particular their wind and magnetospheres. As the star rotates it will be possible to reconstruct 3D maps of the star and its surroundings. The second goal of UVMag is to obtain two observations of a large sample of stars to construct a new database of UV and optical spectropolarimetric measurements.