The `International Heidelberg Workshop on TeV Gamma-Ray Astrophysics' brought together astrophysicists from the various fields which play a role in the formation of high energy gamma-ray emission. In particular, theoretical and observational aspects of the physics and astrophysics of pulsars and quasars, the acceleration of particles at Supernova Remnants and other strong astrophysical shock fronts, and cascade processes in universal background photon fields were comprehensively discussed in more than thirty reviews by leading experts. In their entirety these reviews describe the birth of a new field of astronomy. This field concerns cosmic gamma-rays of very high energy which are observed with ground-based optical telescopes due to the Cherenkov emission of the secondary particles created by the interaction of these gamma-rays with atoms in the Earth's atmosphere. Beyond that, the workshop encompassed the latest developments and trends in theory and observation of cosmic gamma-ray sources of all energies, from nuclear gamma-ray lines in the MeV-region, through the Bremsstrahlung, Inverse Compton, and pion decay continuum emission, to gamma-rays due the decay of exotic relics from the early Universe. Audience: Specialists as well as students in physics and astrophysics and young research workers.