The author of the book tries to analyze the ideas related to the concept of safety: threat, accident, probability, damage, risk. In the system of these concepts, classifications of the most important of them are proposed. Specific examples of existing methods of their calculation are considered. Based on the practice of justifying safety in the use of nuclear energy, ways to improve quantitative methods of safety assessments, methods for calculating the probabilities and risk of accidents are outlined. Nuclear and radiation safety indicators were analyzed, and on the basis of the proposed classification, the main ones were identified to assess the effectiveness of regulatory activities and the safety of nuclear facilities.