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Fermi surfaces, three-dimensional (3D) abstract interfaces that define the occupied energies of electrons in a solid, are important for characterizing and predicting the thermal, electrical, magnetic, and optical properties of crystalline metals and semiconductors. Angle-resolved photoemission spectroscopy (ARPES) is the only technique directly probing the Fermi surface by measuring the Fermi momenta (kF) from energy and angular distribution of photoelectrons dislodged by monochromatic light. Existing electron analyzers are able to determine a number of kF-vectors simultaneously, but current technical limitations prohibit a direct high-resolution 3D Fermi surface mapping. As a result, no such datasets exist, strongly limiting our knowledge about the Fermi surfaces and restricting a detailed comparison with the widely available nowadays calculated 3D Fermi surfaces. Here we show that using a simpler instrumentation, based on the Fourier electron optics combined with a retardation field of the detector, it is possible to perform 3D-mapping within a very short time interval and with very high resolution. We present the first detailed experimental 3D Fermi surface recorded in the full Brillouin zone along the kz-direction as well as other experimental results featuring multiple advantages of our technique. In combination with various light sources, including synchrotron radiation, our methodology and instrumentation offer new opportunities for high-resolution ARPES in the physical and life sciences.