Pairing is the fundamental requirement for fermionic superfluidity and superconductivity. To understand the mechanism behind pair formation is an ongoing challenge in the study of many strongly correlated fermionic systems. Here, we directly observe Cooper pairs in a mesoscopic two-dimensional Fermi gas. We apply an imaging scheme that enables us to extract the full in-situ momentum distribution of a strongly interacting Fermi gas with single particle and spin resolution. Our ultracold gas allows us to freely tune between a completely non-interacting, unpaired system and weak attractions, where we find Cooper pair correlations at the Fermi surface. When increasing the attractive interactions even further, the pairs gradually turn into deeply bound molecules breaking up the Fermi surface. Our observables provide new opportunities to address questions concerning mesoscopic systems that have been raised in nuclear, atomic and condensed matter physics.