We introduce a method to experimentally measure the monochromatic transmission matrix of a complex medium in optics. This method is based on a spatial phase modulator together with a full-field interferometric measurement on a camera. We determine the transmission matrix of a thick random scattering sample. We show that this matrix exhibits statistical properties in good agreement with random matrix theory and allows light focusing and imaging through the random medium. This method might give important insight into the mesoscopic properties of a complex medium. DOI: 10.1103/PhysRevLett.104.100601 PACS numbers: 05.60.Cd, 71.23.-k, 78.67.-n The propagation of waves in heterogeneous media, especially in the multiple-scattering regime, is a very fundamental problem of physics with numerous applications ranging from solid-state physics and optics, to acoustics and electromagnetism [1]. The behavior of such media is usually described by their average macroscopic properties which can be obtained through intensity measurements using, for example, speckle pattern correlations [2] or coherent back scattering experiments [3,4].A deeper approach for the study of complex media lies in the transmission matrix (TM) retrieval. This matrix is a subpart of the usual scattering matrix as defined in [5] for instance. Within this framework, the Green's function between an array of sources and an array of sensors is recorded in transmission. The knowledge of the TM brings more fundamental insight into the medium. One can for instance extract from the TM the single and the multiple-scattering component [6], the backscattering cone, and the field-field correlations [7,8]. The distribution of the singular values of the TM should also be related to the diffusion properties and might exhibit a coherence effect beyond the diffusive transport regime such as weak and strong localization effects.Furthermore, from an operative point of view, the knowledge of the TM of a complex medium offers new and exciting possibilities. For instance, using Time Reversal (TR), it has been shown that multiple scattering, far from limiting wave manipulation through a random medium, can in fact greatly enhance it. Such approaches, which are based on the reciprocity and the reversibility of the wave equations [9], have proved very useful in various areas ranging from focusing to imaging or telecommunication, in acoustic [10][11][12], electromagnetic [13,14] or even seismology [15].For acoustic (electromagnetic) waves, transducers (antennas) are natural local receivers and emitters in phase and amplitude, and oscillation frequencies are compatible with electronic detection. Therefore, the TM can be straightforwardly measured. In contrast, reconstructing the transmission matrix of a complex medium is still an elusive problem in the optical domain.Nonetheless some recent experiments have demonstrated that it is possible to manipulate light at a mesoscopic level in a complex medium in order to focus light through [16] or in [17] a scattering medium, as well as c...