The conventional resolution criterion of an optical instrument was established at the end of the nineteen century in the classical works of Abbe and Rayleigh. This classical limit is based on the presumed resolution capacity of a human eye and is not a fundamental physical limit as, for example, the Heisenberg uncertainty relation. Classical super-resolution techniques allow under certain conditions to go beyond the Rayleigh limit. In this lecture we shall present the quantum theory of optical super-resolution in terms of the prolate spheroidal wave functions. We shall demonstrate that the ultimate limit of super-resolution is determined by the quantum fluctuations of light in the region of the object location and the vacuum fluctuations outside it. We shall formulate the standard quantum limit of super-resolution and show that one can go beyond this limit using spatially multimode squeezed light.