  The project of a micro-TPC matrix of chambers of He3 for direct detection of
non-baryonic dark matter is outlined. The privileged properties of He3 are
highlighted. The double detection (ionization - projection of tracks) will
assure the electron-recoil discrimination. The complementarity of MIMAC-He3 for
supersymmetric dark matter search with respect to other experiments is
illustrated. The modular character of the detector allows to have different
gases to get A-dependence. The pressure degreee of freedom gives the
possibility to work at high and low pressure. The low pressure regime gives the
possibility to get the directionality of the tracks. The first measurements of
ionization at very few keVs for He3 in He4 gas are described.
