Introduction 696 1. Radiation Mechanisms 697 1.1. Processes Leading to the Production of Gamma and X Rays 697 1.2. General Expressions for the Radiation Intensity 698 2. Cosmic Rays, Matter, and Thermal Radiation in the Universe 698 2.1. Intensity of Cosmic Rays 698 2.2. Electronic Component of Cosmic Rays 699 2.3. Matter and Thermal Radiation in the Galaxy and Metagalaxy 700 3. Cosmic Gamma Emission (Calculation of Intensity) 701 3.1. Production of π0 Mesons and "Pionic" Gamma Rays 701 3.2. Bremsstrahlung 702 3.3. Compton Gamma Rays 703 3.4. Positron Annihilation 704 3.5. Nuclear Gamma Rays 706 3.6. Absorption of Gamma and X Rays 706 4. Cosmic Gamma Radiation (Discussion) 707 4.1. Intensity of Over-all Cosmic Gamma Radiation 707 4.2. Gamma Radiation from Discrete Sources 710 4.3. Experimental Data, Their Evaluation, and a Few Conclusions 711 5. X Radiation Connected with Cosmic Rays 713 5.1. Cyclotron X Radiation 713 5.2. X Radiation Due to Other Processes 716 5.3. Comparison of Calculations with Observations 717 Conclusion 718