A method for automatic focusing of a microscope with a microscope objective on a selected area of a specimen, in which a digital hologram of the selected area of the specimen is generated in an off-axis mode and a microscope with which the method is implemented. The digital hologram is used to determine, on the optical axis of the microscope objective, a focus position to be set in which the selected area of the specimen is optimally in focus. Subsequently, a control system is used to set the microscope to the focus position determined and thus is focused on the area selected.