I will describe the Africa Millimetre Telescope (AMT), which is planned to be built on top of the Gamsberg in Namibia and be operational in 2028. As the first millimetre telescope in Africa, the primary focus is to enhance observations of the Event Horizon Telescope. The AMT will facilitate dynamic image reconstructions of Sgr A* and improve our current GR, plasma, accretion, and jet physics tests.Centimetre wavelength receivers for the AMT are planned to be added in the future. This will enable participation in VLBI astrometric observations with the EVN and AVN. I will also describe more exploratory astrometric applications at the shorter millimetre wavelengths. Here, black hole shadows can serve as reliable reference points, unaffected by core-shift effects that have to be taken into account for astrometry with active galactic nuclei at lower observing frequencies. Finally, mm VLBI in-beam phase referencing will be able to improve the astrometry of our galactic centre, particularly the alignment of galactic radio and infrared reference frames. Here, the advantage is that the short wavelength observations are less affected by the interstellar scattering screen towards Sgr A*.