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This book, together with its companion volume The Science of Crystallization: Macroscopic Phenomena and Defect Generation, make up a complete course that will teach an advanced student how to understand and analyse scientifically any of the phenomena that are observed during natural or technological crystallization from any medium and via any technique of crystallization. It is an advanced text that goes into considerable detail concerning the many elements of knowledge needed to understand quantitatively a crystallization event. This particular volume deals with the important atomistic-level processes occurring at the interface between a crystal and its nutrient. It also provides the necessary scientific background of both thermodynamics and kinetics needed for the understanding of crystallization for both bulk crystals and thin film formation.