The European X-ray Free-Electron Laser Facility in Germany delivers x-ray pulses with femtosecond pulse duration at a repetition rate of up to 4.5 MHz. The free-electron laser radiation is created by the self-amplified spontaneous emission (SASE) process, whose stochastic nature gives rise to shot-to-shot fluctuations in most beam properties, including spectrum, pulse energy, spatial profile, wavefront, and temporal profile. Each spectrum consisting of many spikes varies in width and amplitude that appear differently within the envelope of the SASE spectrum. In order to measure and study the SASE spectrum, the HIgh REsolution hard X-ray single-shot (HIREX) spectrometer was installed in the photon tunnel of the SASE1 undulator beamline. It is based on diamond gratings, bent crystals as a dispersive element, and a MHz-repetition-rate strip detector. It covers a photon energy range of 3 keV–25 keV and a bandwidth of 0.5% of the SASE beam. The SASE spikes are resolved with 0.15 eV separation using the Si 440 reflection, providing a resolving power of 60 000 at a photon energy of 9.3 keV. The measured SASE bandwidth is 25 eV. In this paper, we discuss the design specifications, installation, and commissioning of the HIREX spectrometer. The spectral results using Si (110), Si (111), and C (110) crystals are presented.