This lecture provides an introduction to phase transformations in materials science and engineering. It covers the fundamental concepts of phase transformations, including thermodynamics, phase diagrams, and the mechanisms of solidification and crystallization. The instructor discusses the classification of phase transformations into first and second order, highlighting their characteristics and examples. The lecture also delves into the Ising model to illustrate phase transitions and collective effects in materials. Additionally, it addresses the significance of phase transformations in various applications, such as memory materials and the mechanical properties of metals and alloys. The importance of understanding these transformations for the development of new materials is emphasized, along with the role of external conditions like temperature and stress in triggering these changes. Overall, this lecture serves as a foundational overview for students in materials science, providing essential knowledge for further studies in the field.