One of the most promising avenues for the detailed study of temperate Earth-sized exoplanets is the detection of such planets in transit in front of stars that are small and near enough to make it possible to carry out a thorough atmospheric characterisation with next-generation telescopes, such as the James Webb Space telescope (JWST) or Extremely Large Telescope (ELT). In this context, the TRAPPIST-1 planets form a unique benchmark system that has garnered the interest of a large scientific community. The SPECULOOS survey is an exoplanet transit survey targeting a volume-limited (40pc) sample of ultracool dwarf stars (of spectral type M7 and later) that is based on a network of robotic 1m telescopes especially designed for this survey. The strategy for brighter and earlier targets leverages its synergy with the ongoing TESS space-based exoplanet transit survey. We define the SPECULOOS target list as the sum of three non-overlapping sub-programmes incorporating the latest type objects (Teff<3000K). Programme1 features 365 dwarfs that are small and near enough to make it possible to detail atmospheric characterisation of an 'Earth-like' planet with the upcoming James Webb Space Telescope (JWST). Programme2 features 171 dwarfs of M5-type and later for which a significant detection of a planet similar to TRAPPIST-1b should be within reach of TESS. Programme3 features 1121 dwarfs that are later than M6-type. These programmes form the basis of our statistical census of short-period planets around ultracool dwarf stars. Our compound target list includes 1657 photometrically classified late-type dwarfs, with 260 of these targets classified, for the first time, as possible nearby ultracool dwarf stars. Our general observational strategy was to monitor each target between 100 and 200hr with our telescope network, making efficient use of the synergy with TESS for our Programme2 targets and a proportion of targets in our Programme1. Based on Monte Carlo simulations, we expect to detect up to a few dozen temperate, rocky planets. We also expect a number of them to prove amenable for atmospheric characterisation with JWST and other future giant telescopes, which will substantially improve our understanding of the planetary population of the latest-type stars.