Context. The SOLar SPECtrum (SOLSPEC) experiment is part of the Solar Monitoring Observatory (SOLAR) payload, and has been externally mounted on the Columbus module of the International Space Station (ISS) since 2008. SOLAR/SOLSPEC combines three absolutely calibrated double monochromators with concave gratings for measuring the solar spectral irradiance (SSI) from 166 nm to 3088 nm. This physical quantity is a key input for studies of climatology, planetary atmospheres, and solar physics. Aims. A general description of the instrument is given, including in-flight operations and performance of the ultraviolet (UV) channel from 175 nm to 340 nm. Methods. We developed a range of processing and correction methods, which are described in detail. For example, methods for correcting thermal behavior effects, instrument linearity, and especially the accuracy of the wavelength and absolute radiometric scales have been validated by modeling the standard uncertainties. Results. The deliverable is a quiet Sun UV reference solar spectrum as measured by SOLAR/SOLSPEC during the minimum of solar activity prior to cycle 24. Comparisons with other instruments measuring SSI are also presented.