This Ph. D. thesis reports on the first Bose-Einstein condensation of molecules starting from optically trapped fermionic 6Li atoms. The control over the interaction properties by means of a Feshbach resonance allowed us to pair the fermionic atoms to bosonic 6Li2 molecules that were Bose condensed by evaporative cooling. The molecular condensate with its tunable interactions was a major breakthrough for the study of ultracold Fermi gases.
