Hypernuclear physics adresses the baryon-baryon interaction under flavored-SU(3) with up, down and strange quarks. Hypernuclei have been so far studied mainly by induced reactions of meson- or electron-beams. In these experiments, an excellent energy resolution has been achieved, however, the isospin of the produced hypernuclei has been limited by the availability of target materials. We, the HypHI collaboration, has proposed precise hypernuclear spectroscopy with heavy ion induced reactions by producing and identifying hypernuclei as a projectile fragment. With this technique, studies of hypernuclei at extreme isospin as well as hypernuclear magnetic moments could be reached. We have already performed the Phase 0 experiment with Li-6 projectiles at 2 A GeV impinging in a carbon target in order to demonstrate the feasibility of the experimental method. We have already succeeded to produce and identify three- and four-body Lambda hypernuclei. In addition, an indication of a possible Lambda-neutron bound state will be also discussed.
