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The HypHI collaboration aims to perform a precise hypernuclear spectroscopywith stable heavy ion beams and rare isotope beams at GSI and fAIR in order tostudy hypernuclei at extreme isospin, especially neutron rich hypernuclei tolook insight hyperon-nucleon interactions in the neutron rich medium, andhypernuclear magnetic moments to investigate baryon properties in the nuclei.We are currently preparing for the first experiment with $^6$Li and $^{12}$Cbeams at 2 AGeV to demonstrate the feasibility of a precise hypernuclearspectroscopy by identifying $^{3}_{\Lambda}$H, $^{4}_{\Lambda}$H and$^{5}_{\Lambda}$He. The first physics experiment on these hypernuclei isplanned for 2009. In the present document, an overview of the HypHI project andthe details of this first experiment will be discussed.

The HypHI project: Hypernuclear spectroscopy with stable heavy ion beams and rare isotope beams at GSI and FAIR