This volume consists of invited lectures and seminars presented at the NATO Advanced Study Institute The Gamma Ray Sky with COMPTON GRO and SIGMA , which was held at the Centre de Physique Theorique of Les Houches (France) in January / February 1994. The school has been planned by a Scientific Organizing Committee. It was organized with the aim of providing students and young researchers with an up-to-date account of the high-energy phenomena in the vicinity of compact objets and the diffuse gamma-ray backgrounds after the early results from the gamma-ray telescope SIGMA and the four instruments onboard COMPTON GRO (Gamma Ray Observatory) : BATSE (Burst and Transient Source Experiment),COMPTEL(Compto'l Telescope),EGRET (Energetic Gamma Ray Experiment Telescope) and OS SE(Oriented Scintillation Spectrometer Experiment) . It was attended by more than sixty researchers from many countries. The lectures and seminars represent a complete coverage of our present knowledge and understanding of: Gamma-ray backgrounds, Gamma-ray Burts,Active Galactic Nuclei,Galactic Compact Objects, Gamma-ray Spectroscopy, Instrumentation and observation techniques, etc ... Most of these lectures are reproduced in this volume. Unfortunately, a few lecturers have chosen not to submit their manuscript.