The design and realization of a stigmatic grazing-incidence instrument for space applications to solar imaging spectroscopy is presented. We propose an optical layout in which imaging and spectral capabilities are decoupled by the use of crossed cylindrical mirrors. The design consists of a double telescope and a spectrograph: telescope I consists of a single cylindrical mirror with parabolic section, focusing the radiation on the entrance slit of the spectrograph in the spectral dispersion plane; telescope II consists of two cylindrical mirrors with aspherical section in Wolter configuration focusing the radiation on the spectrograph focal plane in the direction perpendicular to the spectral dispersion plane; the spectrograph consists of a grazing-incidence spherical variable-line-spaced grating with flat-field properties. Telescope II is crossed with respect to the grating and telescope I, i.e., is mounted with its tangential planes coincident with the grating equatorial plane, to decouple spectral and spatial focusing properties. The spectral resolution is preserved also for off-axis angles. The instrument that has been realized operates in the 4-26 nm spectral range and has a field of view of 0.5 deg to image the full Sun disk.