The High Acceptance Di-Electron Spectrometer HADES has been commissioned recently at GSI Darmstadt. This detector has been designed to study hadron properties inside nuclear matter via measurements of their di-electron decays in proton, pion and heavy-ion induced reactions in the few-GeV bombarding energy range. The physics program is largely motivated by the aim to study medium modifications of hadrons predicted by many theoretical approaches, as well as by the need to shed light on the still unexplained results of the former DLS experiment. In our contribution, the HADES experiment and the analysis techniques used will be outlined. Next, our results obtained in 12C+12C collisions at 2 AGeV will be presented in detail. Furthermore, the measured di-electron mass distributions will be compared with realistic simulations based on dilepton production models.