The ASTRI (Italian Replicating Technology Mirror Astronomy) program was born as a flagship project of MIUR with INAF leadership and aimed at the technological development of the next generation of Imaging Atmospheric Cherenkov Telescopes (IACTs) for very high energy gamma astronomy (> 10 GeV ), in light of the development of the Cherenkov Telescope Array Observatory (CTAO) [Pareschi et al. 2013] The acronym ASTRI was coined by Nanni Bignami (President of INAF at that time and a great supporter of the project) and it is closely linked to the production process of the primary mirror segments. The project involves more than 150 researchers of the INAF institutes in Bologna, Catania, Milan, Padua, Palermo and Rome, the universities of Perugia, Padua, Catania, Genoa and Milan together with the INFN sections of Perugia and Rome Tor Vergata. The international partners of the project are the University of Sao Paulo in Brazil, the North Western University in South Africa and the Instituto de Astrofisica de Canarias (IAC) in Spain. The first phase of the project consisted in the design, construction and deployment of a Small Size Telescope prototype with a 4m primary mirror, inaugurated in 2014 at the Serra La Nave observatory (Catania, Sicily) and called ASTRI-Horn in honor of Guido Horn-D'Arturo, the Italian scientist who introduced the idea of segmented mirrors now exploited mainly in gamma astronomy. The prototype was validated with the first detection of the Crab with a Cherenkov telescope in a dual-mirror Schwarzschild-Couder configuration [Lombardi et al. 2020]. The structure of this prototype was chosen for the development of the Small Size Telescopes in CTA. After the realization and validation of the ASTRI-Horn prototype, the project moved forward with the idea of the ASTRI Mini-Array, an array of 9 Small Size Telescopes almost identical to ASTRI-Horn, which would have had the role of pathfinder for the South site of CTA. How-ever, the CTA timeline was not compatible with the ASTRI funds availability, so in 2019 INAF and the Instituto de Astrofisica des Ca-narias (IAC) came to an agreement to install the ASTRI Mini-Array at the Teide Astronomical Observatory, operated by IAC, in the Canary island of Tenerife. The first three telescopes will be operational by early 2024 (the first one is already in the site waiting the camera) and the entire array will be complete by 2025. In the meantime, many scientific simulations have been carried out (with related publications) to show how the performances of this instrument can answer many of the still open questions in high energy astrophysics. ASTRI Mini-Array will in fact have an unprecedented sensitivity and angular resolution for energies greater than 10 TeV that will allow not only to understand the nature of the gamma emission revealed by galactic and extragalactic astrophysical objects, obtaining better spectral data at higher energies but also solving their morphology, a fundamental point in the multi-wavelength analysis and in the study of the acceleration mechanisms that produce the detected emission (see particle acceleration project).