THESEUS, one of the two space mission concepts being studied by ESA as candidates for next M5 mission within its Comsic Vision programme, aims at fully exploiting Gamma-Ray Bursts (GRB) to solve key questions about the early Universe, as well as becoming a cornerstone of multi-messenger and time-domain astrophysics. By investigating the first billion years of the Universe through high-redshift GRBs, THESEUS will shed light on the main open issues in modern cosmology, such as the population of primordial low mass and luminosity galaxies, sources and evolution of cosmic re-ionization, SFR and metallicity evolution up to the “cosmic dawn” and across Pop-III stars. At the same time, the mission will provide a substantial advancement of multi-messenger and time-domain astrophysics by enabling the identification, accurate localisation and study of electromagnetic counterparts to sources of gravitational waves and neutrinos, which will be routinely detected in the late ‘20s and early ‘30s by the second and third generation Gravitational Wave (GW) interferometers and future neutrino detectors, as well as of all kinds of GRBs and most classes of other X/gamma-ray transient sources. Under all these respects, THESEUS will provide great synergies with future large observing facilities in the multi-messenger domain. A Guest Observer programme, comprising Target of Opportunity (ToO) observations, will expand the science return of the mission, to include, e.g., solar system minor bodies, exoplanets, and AGN.