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In this chapter, we give a general view of the formation of the solid from its melt. This process is generally driven by the extraction of heat from the melt but fluid flow has a major influence on solidification. Thus an early section deals with transport phenomena. Phase diagrams and the associated thermodynamics data bases and software play a major role in solidification and so a subsequent section treats this topic. The following sections treat nucleation, interface attachment kinetics, solute distribution, cellular and dendritic growth and polyphase solidification. Subsequently, the effect of flow on the grain structure of castings, macrosegregation and porosity are treated. Finally we provide a discussion of developing processes employing various aspects of soldification.