1. A microscope for high-resolution luminescence microscopy of a sample marked with marking molecules that can be activated in such a manner that, once activated, the marking molecules can be excited to emit particular luminescent radiation, wherein the microscope comprises: a) an illumination beam path formed for repeated activation and excitation of a subset of the marking molecules to emit luminescent radiation at least some of the luminescent marking molecules at least at a distance from the luminescent marking molecules immediately adjacent thereto greater than or equal to a minimum resolvable length which results from a predetermined optical resolution; b) an imaging device including an objective and a detector, the imaging device being configured to repeatedly image the sample along a depth direction and with the predetermined optical resolution; c) a control and evaluation device, including a computer, operably coupled to the imaging device and programmed with an algorithm that produces individual images based on data received from the imaging device and determines the geometrical locations of the luminescent marking molecules in the individual images with a spatial resolution which is increased above the predetermined optical resolution; wherein d) the illumination beam path introduces the activation and/or excitation radiation into at least two regions, the regions each extending along a plane substantially perpendicular to the depth direction, the regions having a predetermined extent in the depth direction, and the regions arranged in such a manner that said regions are one behind another in the depth direction and overlap only partially; and wherein e) the imaging device is configured to capture separate images of the sample for activation and/or excitation of each of the at least two regions and the control and evaluation device obtains a depth information relating to the marking molecules from the separate images.