This thesis reports on the preparation of a 2D Fermi gas in the BEC-BCS crossover and \nthe observation of the BKT transition into a quasi long-range ordered superfluid phase. \nThe pair momentum distribution of the gas is probed by means of a matter-wave \nfocusing technique which relies on time-of-flight evolution in a weak harmonic potential. \nThis distribution holds the coherence properties of the gas. \nThe quasi long-range ordered phase manifests itself as a sharp low-momentum peak. \nThe temperature where it forms is identified as the transition temperature. By tuning \nthe temperature and the interaction strength, the phase diagram of the 2D Fermi gas in \nthe BEC-BCS crossover is mapped out. \nThe phase coherence is investigated in a self-interference experiment. Furthermore, \nalgebraic decay of correlations is observed in the trap average of the first order corre- \nlation function, which is obtained from the Fourier transform of the pair momentum \ndistribution. This is in qualitative agreement with predictions of homogeneous theory \nfor the superfluid phase in a 2D gas. \nThe presented results provide a foundation for future experimental and theoretical \nstudies of strongly correlated 2D Fermi gases. They might thus help to elucidate complex \nsystems such as the electron gas in high-Tc superconductors.