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The nuclear reactions occurring in the cores of stars which are believed to produce the element oxygen are first described. Evidence for the absence of free oxygen in the early atmosphere of the earth is reviewed. Mechanisms of creation of atmospheric oxygen by photochemical processes are then discussed in detail. Uncertainty regarding the rate of diffusion of water vapor through the cold trap at 70 km altitude in calculating the rate of the photochemical production of oxygen is avoided by using data for the concentration of hydrogen atoms at 90 km obtained from the Meinel OH absorption bands. It is estimated that the present atmospheric oxygen content could have been produced five to ten times during the earth's history. It is shown that the isotopic composition of atmospheric oxygen is not that of photosynthetic oxygen. The fractionation of oxygen isotopes by organic respiration and oxidation occurs in a direction to enhance the O18 content of the atmosphere and compensates for the O18 dilution resulting from photosynthetic oxygen. Thus, an oxygen isotope cycle exists in nature.