The kinetics of crystallization of a magma body can be described in terms of the classic Johnson-Mehl-Avrami expression for the rate of crystallization of nucleation and growth-controlled reactions combined with the heat flow equation including a term for the rate of release of latent heat. Although present data for the rates of nucleation and growth in geologic systems are insufficient to warrant quantitative calculations, finite differences solutions of these equations using reasonable values for these rates predict qualitatively many of the observed features in natural systems. These observed features include the variation in mineral composition and crystal morphology with distance from a surface of cooling and fraction crystallized, the form of the fraction crystallized versus time curve, and the relationships between the rates of nucleation and growth and the fraction crystallized. More detailed calculations will require accurately determined values for the appropriate rates of nucleation and growth and a knowledge of the process by which nucleation takes place.