A nucleation rate function is proposed for use in analyzing the overall crystallization kinetics of polymers. This function allows for the possibility that the nucleation rate varies substantially during the crystallization. This feature is particularly useful in analyzing nonisothermal crystallization, but it can be used to analyze isothermal crystallization as well. The nucleation rate function was used in the derivation of a modified transformation kinetics equation of the Avrami type. The modified Avrami equation was found to be suitable for kinetics analysis for the data obtained from nonisothermal crystallization at rapid cooling rates. Kinetics parameters used to describe nonisothermal crystallization under rapid cooling rates are presented and discussed. These include crystallization induction time, plateau (crystallization) temperature, crystallization half-time, crystallization rate constant, Avrami index, and newly defined quantities called nucleation index, geometric index, and nucleation rate constant. The procedure used to obtain the nucleation rate constant and nucleation index for the nucleation rate function is described and illustrated by application to the analysis of the crystallization kinetics of polypropylene.