In this chapter, we will discuss the kinetics of the cooling crystallization of magma, i.e., nucleation and growth, to use it as a foundation for making tools for observing unknown information from crystallization texture similar to the vesiculation processes (equilibrium conditions Chap. 2, nucleation process Chap. 3, growth process Chap. 4, temporal development of vesiculation Chap. 5, and complex processes related to vesiculation Chap. 6) dealt with in previous chapters. In this chapter, for crystallization-related problems, we will explain the similar contents in one go because both vesiculation and crystallization are the formation of a new phase from solution or a phase transition process and have similarity. First, using a binary eutectic system as an example of a multi-component system, we will explain crystallization-related conditions from a liquid and define a solid—liquid equilibrium as well as supersaturation in terms of thermodynamics. Next, we will conduct the formulation of crystal nucleation and crystal growth, evaluate experiments using these results, and examine the classical theory. As the crystal growth-related problems, the compositional zoning that is often observed in crystals is discussed for simplified cases, involving the movement of the interface, which has been extensively studied in metallurgy.