The questions addressing the nature of atmospheric ozone, the chemicals that cause ozone depletion, and what could lie ahead for the ozone layer are discussed. The role of the ozone layer to prevent from the Sun’s UV radiation is discussed. A detailed research program package of problems for mathematical simulation of ozone kinetics is developed. A wide variety of integration methods for systems of differential equations is involved. Methods can compare calculation results or can be checked manually to increase solution speed for complex systems of differential equations.