This important book delineates experimental studies of effects of low dose irradiation on biological objects (organisms, cells, and biomolecules and presents theoretical concepts related to the issue. The problem of low dose irradiation has many aspects: theoretical (what is truth), populist, political, and bureaucratic (low doses versus the atomic industry). The book contains important works dealing with one of important effects of low dose irradiation -- an adaptive response. It is known that a subsequent high dose of irradiation of cells and organisms irradiated earlier with low doses causes lesser damages than after irradiation with high dose. Some of the authors consider a dependence of an adaptive response on a radiation dose and dose rate and on a time span between the first exposure to an adaptive dose and the second one. Scientists who believe in a radiobiological dogma that the higher the dose and the dose-rate, the stronger the effect, cannot explain the observed changes in the state of health by the irradiation effects and try to discover other factors responsible for these changes. It is concluded that low doses of radiation are indeed dangerous because low doses, above all, affect our sensitivity to the action of other damaging factors of the endogenic and exgenic nature. A number of these environmental factors is considerable. Their effect is evidently not fatal and we can be protected from them by making efforts to study the specific effects of low doses instead of verbal discussion about whether low doses affect the organism, cells, and population or not.