The ASTRI Mini-Array is an INAF project to build and operate a facility to study astronomical sources emitting very high energy in the TeV spectral band. It consists of a group of nine innovative aplanatic dual mirror Imaging Atmospheric Cherenkov Telescopes (IACT) of 4 m diameter. The telescopes are being installed at the Teide Astronomical Observatory of the Instituto de Astrofisica de Canarias in Tenerife (Canary Islands, Spain) based on a host agreement with INAF. Thanks to its expected overall performance, better than those of current IACT arrays, for energies above about 5 TeV and up to 100 TeV and beyond, the ASTRI Mini-Array will represent an important instrument to perform deep observations of the Galactic and extra-Galactic sky at these energies with high angular resolution (a few arcmins). It will be complementary to the wide-field particle shower arrays (based on water Cherenkov and scintillator detectors) like HAWC and LHAASO already operated in the northern hemisphere. The ASTRI Mini-Array is currently under construction and in this paper, we will present its status, discussing its design and expected performance.