  These notes present the fundamentals of Fermi acceleration at shocks, with a
special attention to the role that supernova remnants have in producing
Galactic cosmic rays. Then, the recent discoveries in the theory of diffusive
shock acceleration (DSA) that stem from first-principle kinetic plasma
simulations are discussed. When ion acceleration is efficient, the
back-reaction of non-thermal particles and self-generated magnetic fields
becomes prominent and leads to both enhanced shock compression and particle
spectra significantly softer than those predicted by the standard test-particle
DSA theory. These results are discussed in the context of the non-thermal
phenomenology of astrophysical shocks, with a special focus on the remnant of
SN1006.
