e-ASTROGAM is a concept for a breakthrough observatory space mission carrying a γ-ray telescope dedicated to the study of the non-thermal Universe in the photon energy range from 0.15 MeV to 3 GeV. The lower energy limit can be pushed down to energies as low as 30 keV for gamma-ray burst detection with the calorimeter. The mission is based on an advanced space-proven detector technology, with unprecedented sensitivity, angular and energy resolution, combined with remarkable polarimetric capability. Thanks to its performance in the MeV–GeV domain, substantially improving its predecessors, e-ASTROGAM will open a new window on the non-thermal Universe, making pioneering observations of the most powerful Galactic and extragalactic sources, elucidating the nature of their relativistic outflows and their effects on the surroundings. With a line sensitivity in the MeV energy range one to two orders of magnitude better than previous and current generation instruments, e-ASTROGAM will determine the origin of key isotopes fundamental for the understanding of supernova explosion and the chemical evolution of our Galaxy. The mission will be a major player of the multiwavelength, multimessenger time-domain astronomy of the 2030s, and provide unique data of significant interest to a broad astronomical community, complementary to powerful observatories such as LISA, LIGO, Virgo, KAGRA, the Einstein Telescope and the Cosmic Explorer, IceCube-Gen2 and KM3NeT, SKA, ALMA, JWST, E-ELT, LSST, Athena, and the Cherenkov Telescope Array.