  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.
