We introduce and study a novel concept in farfield fluorescence microscopy fundamentally overcoming the classical diffraction resolution limit. This is accomplished by reducing the spatial extent of the effective focus of a scanning fluorescence microscope. The reduction is achieved by depleting the ground-state energy of the molecules located in the outer region of the focus. Our theoretical study shows that ground-state-depletion fluorescence microscopy has the potential of increasing the resolution of far-field fluorescence microscopy by an order of magnitude which is equivalent to a lateral resolution of 15 NM.