The ASTRI (Astrofisica con Specchi a Tecnologia Replicante Italiana) Project led by the Italian National Institute for Astrophysics (INAF) is developing and will deploy at the Observatorio del Teide a mini-array (ASTRI Mini-Array) composed of nine telescopes similar to the small-size dual-mirror Schwarzschild-Couder telescope (ASTRI-Horn) currently operating on the slopes of Mt. Etna in Sicily. The ASTRI Mini-Array will surpass the current Cherenkov telescope array differential sensitivity above a few teraelectronvolt (TeV), extending the energy band well above hundreds of TeV. This will allow us to explore a new window of the electromagnetic spectrum, by convolving the sensitivity performance with excellent angular and energy resolution figures. In this paper we describe the Core Science that we will address during the first four years of operation, providing examples of the breakthrough results that we will obtain when dealing with current open questions, such as the acceleration of cosmic rays, cosmology and fundamental physics and the new window, for the TeV energy band, of the time-domain astrophysics.
