The article analyses the concept of «industrial safety», its official definitions and their drawbacks. The more correct definition is formed for «industrial safety». The levels of industrial safety are introduced for observation and their components are systematized. The approaches for quantitative estimation of industrial safety are observed. The necessity of substantiation of space-time parameters of anthropogenic accidents danger is shown as well as the need in introduction of a new high school discipline «The Danger of Anthropogenic Accidents (Catastrophes)».