The emphasis of this book is on the quantitative analysis of transformation kinetics, integrated with thermodynamics. Solidification is a success story for quantitative kinetics analysis. The work reported concentrates on phase selection under extreme processing - large undercooling or ultrarapid quenching - of the liquid. Theoretical treatments are concerned mainly with the analysis of morphological instabilities during directional solidification at more conventional rates. The coverage of particle-beam effects is distinguished by the materials studied: alkali halides, minerals, semiconductors and metals. The thermodynamics of interfaces are a particular focus, especially in connection with the solid-state formation of amorphous phases. A highlight of the book is the coverage of the Johnson-Mehl-Avrami-Kolmogorov analysis of overall transformation kinetics. This venerable treatment is revisited and new insights and limitations are explored. Topics include: transformations in undercooled liquids; directional solidification; particle beam-induced transformations; interfaces - thermodynamics and reactions; amorphous materials - structure and transformations; solid-state transformations and ordering and phase separation.