The Solar Diameter Imager and Surface Mapper (SODISM) onboard the Picard space mission provides wide-field images of the photosphere and chromosphere of the Sun in five narrow bandpasses centered at 215.0, 393.37, 535.7, 607.1, and 782.2 nm. The Picard spacecraft was successfully launched on 15 June 2010 into a Sun-synchronous dawn–dusk orbit. The Picard space mission represents a European asset in collecting solar observations useful to improve Earth climatic models. The scientific payload consists of the SODISM imager and of two radiometers, SOlar VAriability Picard (SOVAP) and PREcision MOnitor Sensor (PREMOS), which measure the Total Solar Irradiance (TSI) and part of the Solar Spectral Irradiance (SSI).The SODISM telescope continuously monitors solar activity from the middle ultraviolet to the near infrared spectral ranges and produces solar images that feed SSI reconstruction models. Further, SODISM probes the solar interior via a helioseismic analysis of the solar disc and limb images at 535.7 nm, and via astrometric investigations at the limb. The latter allows us to deduce the spectral dependence of the solar limb profile, and the asphericity of the Sun. Furthermore, SODISM data taken during the transit of Venus allow a determination of the absolute value of the solar diameter. This paper provides a detailed description of the SODISM instrument, including thermo-optical analysis, its different modes of observation, and its first performance in space.