This provides a brief description of the history of the Stefan problem, followed by the formulation of the governing equations and boundary conditions (including mushy regions) for the classical case. After a discussion of appropriate scales, the system is written in nondimensional form. Parameter values for typical phase change materials are presented, permitting the reader to better understand the physical problem. This sets the scene for subsequent chapters, where the nondimensional system is analysed in a variety of settings and, in later chapters, the governing equations are extended beyond the classical form. This chapter, and all subsequent chapters, ends with a set of exercises (solution outlines are presented at the end of the book).