The main science aim of the BlackGEM array is to detect optical counterparts to gravitational wave mergers. Additionally, the array will perform a set of synoptic surveys to detect Local Universe transients and short time-scale variability in stars and binaries, as well as a six-filter all-sky survey down to ~22nd mag. The BlackGEM Phase-I array consists of three optical wide-field unit telescopes. Each unit uses an f/5.5 modified Dall-Kirkham (Harmer-Wynne) design with a triplet corrector lens, and a 65cm primary mirror, coupled with a 110Mpix CCD detector, that provides an instantaneous field-of-view of 2.7~square degrees, sampled at 0.564\arcsec/pixel. The total field-of-view for the array is 8.2 square degrees. Each telescope is equipped with a six-slot filter wheel containing an optimised Sloan set (BG-u, BG-g, BG-r, BG-i, BG-z) and a wider-band 440-720 nm (BG-q) filter. Each unit telescope is independent from the others. Cloud-based data processing is done in real time, and includes a transient-detection routine as well as a full-source optimal-photometry module. BlackGEM has been installed at the ESO La Silla observatory as of October 2019. After a prolonged COVID-19 hiatus, science operations started on April 1, 2023 and will run for five years. Aside from its core scientific program, BlackGEM will give rise to a multitude of additional science cases in multi-colour time-domain astronomy, to the benefit of a variety of topics in astrophysics, such as infant supernovae, luminous red novae, asteroseismology of post-main-sequence objects, (ultracompact) binary stars, and the relation between gravitational wave counterparts and other classes of transients