  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 tera-electronvolt (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.
