The authors of this book have studied the changes in the chemi- cal composition of the atmosphere during geological history with regard to its close relationship to the evolution of the Earth's sedimentary shell. Beginning in 1977, the initial results of this study have been published as articles and parts of several monographs. Since new material clarifying atmospheric evolution have been obtained recently, the necessity has arisen to write a book treating the major results of investigations of the history of the atmosphere. In this book much consideration is given to the interrelation between the evolution of animate nature and changes in atmospheric composition. It proved be necessary to study the history of the two components of atmospheric air: carbon dioxide and oxygen. Attempts have been made to repre- sent quantitatively the conclusions drawn here, i. e. to determine by calculation the changes in the amount of carbon dioxide and oxygen over much of the history of the atmosphere. These calculations, performed in most detail for the Phanerozoic and to a lesser degree for the Late Precambrian, are supplemented with estimates of changes in the chemical composition of the atmosphere in the Early Precambrian. Comparisons have been drawn between the changes in the chemical composition of the atmosphere and the development of animate nature, a close relationship being found to exist between the stages of the evolution of organisms and variations in the chemical composition of the atmosphere.