Cherenkov telescopes play a major role in the growth of the TeV Astronomy which, in 20 years, has reached the status of an important branch of Astrophysics, because of the observations of the violent, non thermal processes in the extreme band of the electromagnetic spectrum above several tens of GeV up to several tens of TeV. About one hundred extragalactic sources (Active Galactic Nuclei, blazars, and radiogalaxies) and Galactic sources (shell supernovae remnants, pulsar wind nebulae, isolated pulsars, X-ray binaries, and unidentified sources) have been detected so far. In the near future, an ambitious new array, the Cherenkov Compton Telescope (CTA) will substitute the present Cherenkov telescopes arrays. CTA is designed as an array of many (50-100) Cherenkov telescopes operated in stereo mode. CTA will allow to gain a factor of 10 in sensitivity with respect to the present arrays such as H.E.S.S., MAGIC, and VERITAS. Moreover, CTA will connect the TeV to the GeV energy band covered by space missions such as Fermi and AGILE, and will also explore the highest energy region of the electromagnetic spectrum up to several hundreds of TeV.
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