This review article revisits Melvin Avrami's kinetic model for phase change, which was developed in the 1930s. The model describes the temporal behavior of phase changes, particularly the nucleation and growth of new phases. The authors aim to clarify the mathematical treatment of Avrami's work, focusing on the arguments leading to his main results. They introduce the concepts of germs, grains, and transformed volume, and derive equations to describe the variation of these quantities over time. The article also discusses the characteristic time scale and the exact relationship for the swallowed germs. Additionally, it explores the evolution of the extended volume and the relation between real and extended volumes. The authors provide empirical expressions for the transformation kinetics, including the Austin-Rickett formula, and analyze the temporal evolution of the transformation under different conditions. The final result of the model is the fundamental relation \( V = 1 - \exp(-B t^k) \), which is applicable to isokinetic and isothermal phase change transformations. This relation can be used to determine the kinetic law of a phase change by fitting experimental results. The model also allows for the determination of grain dimensions through the ratio of growth times.This review article revisits Melvin Avrami's kinetic model for phase change, which was developed in the 1930s. The model describes the temporal behavior of phase changes, particularly the nucleation and growth of new phases. The authors aim to clarify the mathematical treatment of Avrami's work, focusing on the arguments leading to his main results. They introduce the concepts of germs, grains, and transformed volume, and derive equations to describe the variation of these quantities over time. The article also discusses the characteristic time scale and the exact relationship for the swallowed germs. Additionally, it explores the evolution of the extended volume and the relation between real and extended volumes. The authors provide empirical expressions for the transformation kinetics, including the Austin-Rickett formula, and analyze the temporal evolution of the transformation under different conditions. The final result of the model is the fundamental relation \( V = 1 - \exp(-B t^k) \), which is applicable to isokinetic and isothermal phase change transformations. This relation can be used to determine the kinetic law of a phase change by fitting experimental results. The model also allows for the determination of grain dimensions through the ratio of growth times.