The condensation of fermion pairs lies at the heart of superfluidity. However, for strongly correlated systems with reduced dimensionality the mechanisms of pairing and condensation are still not fully understood. In our experiment we use ultracold atoms as a generic model system to study the phase transition from a normal to a condensed phase in a strongly interacting quasi-two-dimensional Fermi gas. Using a novel method, we obtain the in situ pair momentum distribution of the strongly interacting system and observe the emergence of a low-momentum condensate at low temperatures. By tuning temperature and interaction strength we map out the phase diagram of the quasi-2D BEC-BCS crossover.The characteristics of quantum many-body systems are strongly affected by their dimensionality and the strength of interparticle correlations. In particular, strongly correlated two-dimensional fermionic systems have been of interest because of their connection to high-T c superconductivity. Although they have been the subject of intense theoretical studies [1][2][3][4][5][6][7][8], a complete theoretical framework has not yet been established.Ultracold quantum gases are an ideal realization for exploring strongly interacting 2D Fermi gases, as they offer the possibility of independently tuning the dimensionality and the strength of interparticle interactions. Reducing the dimensionality [9] led to the observation of a Berezinskii-Kosterlitz-Thouless (BKT) type phase transition to a superfluid phase in weakly interacting 2D Bose gases [10,11]. Tuning the strength of interactions in a three-dimensional two-component Fermi gas made it possible to explore the crossover between a molecular Bose-Einstein Condensate (BEC) and a BCS superfluid [12][13][14][15].Recently, efforts have been made to combine reduced dimensionality with the tunability of interactions and to experimentally explore ultracold 2D Fermi gases [16][17][18][19][20][21]. However, the phase transition to a condensed phase has not yet been observed. Here, we report on the condensation of pairs of fermions in the quasi-2D BEC-BCS crossover.The BEC-BCS crossover smoothly links a bosonic superfluid of tightly bound diatomic molecules to a fermionic superfluid of Cooper pairs in 2D as well as 3D systems. However, changing the dimensionality leads to some inherent differences. In two dimensions, there is a two-body bound state for all values of the interparticle interaction. Furthermore, because of the enhanced role of * To whom correspondence should be addressed. E-mail: mries@physi.uni-heidelberg.de † These authors contributed equally to this work. ‡ Present address: MIT-Harvard Center for Ultracold Atoms, MIT, Cambridge, MA 02139, USA.fluctuations in 2D, true long-range order is forbidden for homogeneous systems at finite temperature [22,23]. Still, a low temperature superfluid phase with quasi-long-range order can emerge due to the BKT mechanism [24,25]. In a 2D gas with contact interactions, the interactions can be described by the 2D scattering length a 2D . Using th...