This seminar introduces the time-frequency analysis of Gabor frames and the sampling problem for the Bargmann-Fock space, which is still an open question in the multivariate situation. It is theoretically possible to reconstruct a signal (a square-integrable function) and its Fourier transform, as integral superpositions of time-frequency shifts operators. In practical applications, Gabor theory provides a discrete version of this reconstruction formula, up to a proper choice of a window function and a discrete subset of the phase-space. More precisely, these two objects have to define a frame of L 2 . For several reasons, Gaussian windows are the best suited for the analysis of signals. It turns out that Gaussian frames are characterized by discrete subsets of the phase-space that define sampling sequences for the Bargmann-Fock space, a problem which falls within the realm of complex analysis.