We have observed Bose-Einstein condensation of pairs of fermionic atoms in an ultracold 6_Li gas at magnetic fields below and above a Feshbach resonance. Well below the resonance, the phenomenon is Bose-Einstein condensation of stable molecules. Above the resonance, molecular Bose-Einstein condensates were detected after a fast magnetic field ramp, which transferred pairs of atoms at close distances into bound molecules. Condensate fractions as high as 80% were obtained. The large condensate fractions are interpreted in terms of preexisting molecules, which are quasistable even above the two-body Feshbach resonance due to the presence of the degenerate Fermi gas.
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