The Solar Diameter Imager and Surface Mapper (SODISM) on board the PICARD space mission provides wide-field images of the photosphere and chromosphere of the Sun in five narrow pass bands (centered at 215.0, 393.37, 535.7, 607.1, and 782.2 nm). PICARD is a space mission, which was successfully launched on 15 June 2010 into a Sun synchronous dawn-dusk orbit. It represents a European asset aiming at collecting solar observations that can serve to estimate some of the inputs to Earth climate models. The scientific payload consists of the SODISM imager and of two radiometers, SOVAP (SOlar VAriability PICARD) and PREMOS (PREcision MOnitor Sensor), which carry out measurements that allow estimating the Total Solar Irradiance (TSI) and the Solar Spectral Irradiance (SSI) from the middle ultraviolet to the red. The SODISM telescope monitors solar activity continuously. It thus produces images that can also feed SSI reconstruction models. Further, the objectives of SODISM encompass the probing of the interior of the Sun via helioseismic analysis of observations in intensity (on the solar disc and at the limb), and via astrometric investigations at the limb. The latter addresses especially the spectral dependence of the radial limb shape, and the temporal evolution of the solar diameter and asphericity. After a brief review of its original science objectives, this paper presents the detailed design of the SODISM instrument, its expected performance, and the scheme of its flight operations. Some observations with SODISM are presented and discussed.