The recent launch of NASA's Gamma-Ray Observatory will increase interest in gamma-ray astronomy. This is a fully up-dated new edition of the authors' earlier volume published in 1986 and covers both the background science and the current state-of-the-art in this field. The emphasis is on the astronomy and astrophysics of known sources of cosmic gamma-rays outside the solar system. The authors discuss the mechanisms for the production and absorption of gamma-rays. The gamma-ray line astronomy of the interstellar medium, galactic centre, and various discrete sources is then considered. Gamma-ray bursts are treated in considerable detail in chapter three, and the final two chapters describe medium energy and ultra-high energy gamma-rays. Relevant data from supernova SN1987A is also included in this edition. The book includes comprehensive references to the primary literature, together with many figures and tables. The concentration on phenomenology makes this book a fine introduction to gamma-ray astronomy.