Context. One of the rarest types of variability is the phenomenon of gravitational microlensing, a transient brightening of a background star due to an intervening lensing object. Microlensing is a powerful tool for studying the invisible or otherwise undetectable populations in the Milky Way, including planets and black holes. Aims. We describe the first Gaia catalogue of candidate microlensing events, give an overview of its content, and discuss its validation. Methods. The catalogue of Gaia microlensing events was composed by analysing the light curves of around 2 billion sources of Gaia DR3 from all over the sky covering 34 months, between 2014 and 2017. Results. We present 363 Gaia microlensing events and discuss their properties. Of these, 90 have never been reported before and have not been discovered by other surveys. The contamination of the catalogue is assessed to 0.6%–1.7%.