The concept of risk is now no longer of academic interest only, since it is widely used in legislative acts. In the present paper, risk is defined mathematically as a measure of the possible danger of an object (phenomenon) that can be expressed as a distribution function of a multidimensional random quantity characterizing the different types of possible harm due to the object (phenomenon under study). Some numerical characteristics or parameters of risk are examined. It is shown that using the average value of the consequences of accidents at objects as a risk parameter is of limited application. Various directions of the application of risk to the safety of nuclear power plants are analyzed. The most important application of the methodology of risk analysis is a systems investigation of the "weak links" in safety measures with the generation of recommendations for preventing and limiting the consequences of accidents.
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