The physics of the non-thermal Universe provides information on the acceleration mechanisms in extreme environments, such as black holes and relativistic jets, neutron stars, supernovae or clusters of galaxies. In the presence of magnetic fields, particles can be accelerated towards relativistic energies. As a consequence, radiation along the entire electromagnetic spectrum can be observed, and extreme environments are also the most likely sources of multi-messenger emission. The most energetic part of the electromagnetic spectrum corresponds to the very-high-energy (VHE, E>100 GeV) gamma-ray regime, which can be extensively studied with ground based Imaging Atmospheric Cherenkov Telescopes (IACTs). The results obtained by the current generation of IACTs, such as H.E.S.S., MAGIC, and VERITAS, demonstrate the crucial importance of the VHE band in understanding the non-thermal emission of extreme environments in our Universe. In some objects, the energy output in gamma rays can even outshine the rest of the broadband spectrum. The Cherenkov Telescope Array (CTA) is the next generation of IACTs, which, with cutting edge technology and a strategic configuration of ~100 telescopes distributed in two observing sites, in the northern and southern hemispheres, will reach better sensitivity, angular and energy resolution, and broader energy coverage than currently operational IACTs. With CTA we can probe the most extreme environments and considerably boost our knowledge of the non-thermal Universe.
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