The Cherenkov Telescope Array (CTA) will be the largest ground-based observatory operating in the very-high-energy gamma-ray (20 GeV - 300 TeV) range. It will be based on more than one hundred telescopes, located at two sites (northern and southern hemispheres). The energy coverage, in the southern CTA array, will extend up to hundreds of TeV thanks to 70 small size telescopes (SST), with primary mirrors of about 4 meters in diameter and large field of view of the order of 9 degrees. It is proposed that one of the first sets of precursors for the CTA SSTs array will be represented by nine ASTRI telescopes. Their prototype, named ASTRI SST-2M, is installed in Italy. It is currently completing the overall commissioning before entering the science verification phase that will performed observing bright TeV sources as Crab Nebula, Mrk421 and Mrk 501 cross-checking the prototype performance with the Monte Carlo predictions. ASTRI telescopes are characterized by a dual-mirror optical design based on the Schwarzschild- Couder (SC) configuration. The focal-plane camera is curved in order to fit the ideal prescription for the SC design and the sensors are small size silicon photomultipliers read-out by a fast front-end electronics. The telescope prototype installed in Italy, has been developed by the Italian National Institute for Astrophysics, INAF, following an end-to-end approach that comprises all aspects from the design, construction and implementation of the entire hardware and software system to the final scientific products. All parts of the system have been designed to comply with the CTA requirements. A collaborative effort, addressed to the implementation of the first ASTRI telescopes for the CTA southern site, is now on-going led by INAF with the Universidade de Sao Paulo (Brazil), the North-West University (South Africa) and the Italian National Institute for Nuclear Physics.