In this thesis, two main application fields for off-axis reflection zone plates (RZPs) in X-ray optics were analyzed: as element for the monochromatization of soft and hard X-ray beams and as spectroscopy element for X-ray spectrometers with synchrotron radiation, free electron lasers, as well as laboratory sources such as laser plasma sources and high harmonic generators. As a big step forward in the design process, a new calculation software was developed, using a modern mathematical description of an ellipse-plane intersection. This new approach reduces the data volume and calculation time to a minimum, while ensuring a high accuracy of the structures and opens many possibilities for the design of multi-channel parallel spectrometers for monochromatic and polychromatic radiation. The spectroscopic properties of off-axis RZPs were systematically investigated in the hard X-ray range. The spatial resolution was found to be better than 2 micrometers at 8.3 keV with a diffraction efficiency of 17.5 %. The experimentally tested spectroscopic arrangement showed a resolving power up to 400 in an energy range of 1000 eV around the central energy. This experiment indicates a possibility of absorption spectroscopy on transition metals in the energy range below 10 keV. Simultaneously, a time elongation in the optical element was estimated as 0.35 fs, which would allow ultra-fast time resolved spectroscopy methods. For the first time in the soft x-ray range, within the framework of this thesis, multi-channel RZPs for an ultra-sensitive parallel X-ray spectrometer were realized. Through this development, the spectrometer could be applied at the free electron laser source LCLS in Stanford (outside of this dissertation). The spectroscopy of highly diluted materials, metallo-enzyme complexes that contain manganese oxides, was performed. The new spectrometer has one order of magnitude better acceptance than conventional grating spectrometers. The results of these measurements are not mentioned in this thesis. The developed design model was applied for the realization of two types of new laboratory source spectrometers based on RZPs: a parallel spectrometer for a scanning electron microscope and a single-channel spectrometer for a laser-plasma X-ray source.
