This chapter provides a short introduction to phase transformations, namely, the liquid-to-solid phase transformations that occur during solidification and the solid-to-solid transformations that are important in processing, such as heat treatment. It also introduces the concept of free energy that governs whether or not a phase transformation is possible, and then the kinetic considerations that determine the rate at which transformations take place. The chapter also describes important solid-state transformations such as spinodal decomposition and martensitic transformation.