The Gamma Ray Sky with Compton GRO and SIGMA covers the results of the Compton Gamma Ray Observatory (GRO) satellite, which covers six decades of energy from 15 keV to 30 GeV, the French gamma ray telescope SIGMA, the first imaging experiment on a satellite to observe gamma rays from 35 keV to 1.3 MeV, and of ground-based telescopes in the TeV range. SIGMA and the suite of four instruments aboard the Compton GRO are first described by the members of the Compton GRO Team and the SIGMA science team. Most of the rest of the book is then devoted to the astronomical implications of these observations. The topics covered are: galactic and extragalactic gamma ray sources; galactic and extragalactic gamma ray backgrounds; the galactic centre; gamma ray spectrometry; and gamma ray bursts. Both experimentalists and theoreticians - both astrophysicists and particle physicists - review the achievements, problems and prospects in the gamma ray field, from 15 keV to 1 TeV. The book is also suitable for young scientists working on related topics.