This paper reports the Bose-Einstein condensation (BEC) of more than $10^5$ $Li_2$ molecules in an optical trap, starting from a spin mixture of fermionic lithium atoms. The molecules are formed through three-body recombination near a Feshbach resonance during evaporative cooling and finally condense into a long-lived thermal equilibrium state. The study demonstrates the magnetic-field dependent mean field and the stability of the molecular BEC. The experiment involves evaporative cooling of an optically trapped mixture of fermionic $^6Li$ atoms in the lowest two spin states. During the cooling process, a large number of bosonic dimers are formed by three-body recombination and finally condense into a molecular BEC. The spin mixture exhibits a broad Feshbach resonance at a magnetic field of about 850 G, which leads to a pronounced magnetic-field dependence of the scattering length $a$, characterizing the s-wave interactions. Dimers in a single, weakly bound state can be formed in the range of large positive $a$ with a binding energy of $\hbar^2/(m a^2)$, where $m$ is the mass of a $^6Li$ atom. The experiment shows that the molecular BEC is formed when the scattering length is large and positive, leading to a strikingly different behavior compared to the case of large negative scattering length, where no dimers can be produced. The study demonstrates the formation of a degenerate Fermi gas without the possibility of molecule formation at a magnetic field of 1176 G, where $a \approx -3500a_0$. The evaporation proceeds in a very similar way as described in previous studies. The crossover to Fermi degeneracy occurs when the thermal energy $k_B T$ reaches the Fermi energy $E_F = \hbar \overline{\omega} (3N)^{1/3}$. The formation of molecules during the evaporative cooling process can be understood in terms of a chemical atom-molecule equilibrium. Exothermal three-body recombination processes compete with dissociation by endothermal two-body processes. When the gas is cooled down, the equilibrium shifts to an increasing fraction of molecules. The number of atoms in the two-component spin mixture is given by two times the number of quantum states in the trap. The study confirms this interpretation of the data. The observation that a large number of $N_{mol} \approx 1.5 \times 10^5$ molecules is confined in the trap under thermal equilibrium conditions shows that a molecular BEC is formed. The trap offers about 10 times more quantum states for dimers as compared to the case of atoms. The molecular gas is necessarily quantum degenerate due to the high elastic collision rates. The temperature is a small fraction of the trap depth, and the condensate fraction is given by $1 -This paper reports the Bose-Einstein condensation (BEC) of more than $10^5$ $Li_2$ molecules in an optical trap, starting from a spin mixture of fermionic lithium atoms. The molecules are formed through three-body recombination near a Feshbach resonance during evaporative cooling and finally condense into a long-lived thermal equilibrium state. The study demonstrates the magnetic-field dependent mean field and the stability of the molecular BEC. The experiment involves evaporative cooling of an optically trapped mixture of fermionic $^6Li$ atoms in the lowest two spin states. During the cooling process, a large number of bosonic dimers are formed by three-body recombination and finally condense into a molecular BEC. The spin mixture exhibits a broad Feshbach resonance at a magnetic field of about 850 G, which leads to a pronounced magnetic-field dependence of the scattering length $a$, characterizing the s-wave interactions. Dimers in a single, weakly bound state can be formed in the range of large positive $a$ with a binding energy of $\hbar^2/(m a^2)$, where $m$ is the mass of a $^6Li$ atom. The experiment shows that the molecular BEC is formed when the scattering length is large and positive, leading to a strikingly different behavior compared to the case of large negative scattering length, where no dimers can be produced. The study demonstrates the formation of a degenerate Fermi gas without the possibility of molecule formation at a magnetic field of 1176 G, where $a \approx -3500a_0$. The evaporation proceeds in a very similar way as described in previous studies. The crossover to Fermi degeneracy occurs when the thermal energy $k_B T$ reaches the Fermi energy $E_F = \hbar \overline{\omega} (3N)^{1/3}$. The formation of molecules during the evaporative cooling process can be understood in terms of a chemical atom-molecule equilibrium. Exothermal three-body recombination processes compete with dissociation by endothermal two-body processes. When the gas is cooled down, the equilibrium shifts to an increasing fraction of molecules. The number of atoms in the two-component spin mixture is given by two times the number of quantum states in the trap. The study confirms this interpretation of the data. The observation that a large number of $N_{mol} \approx 1.5 \times 10^5$ molecules is confined in the trap under thermal equilibrium conditions shows that a molecular BEC is formed. The trap offers about 10 times more quantum states for dimers as compared to the case of atoms. The molecular gas is necessarily quantum degenerate due to the high elastic collision rates. The temperature is a small fraction of the trap depth, and the condensate fraction is given by $1 -