Nucleation and the Properties of Undercooled Melts Nucleation is a central topic in Materials Science because it initiates most phase transformations. When a new phase appears within an existing phase seeds must form before growth can occur within the given volume. The study of nucleation treats the very early stages which involve only a limited number of atoms or molecules. It is a branch of fundamental research which has far reaching implications for processes where nucleation is of paramount relevance to phase and microstructure selection. The development of any new material or processing route always leads to renewed interest in the topic. This issue describes the fundamental theory of nucleation as well as the thermophysical properties which most influence its rate. In the first part the classical theory is developed; starting with the heterophase fluctuations which permit the formation of embryos. The latter become crystals only if their size attains a critical value and the associated activation barrier is thus overcome. The second part is devoted to a detailed analysis of those quantities which are related to solidification. The emphasis is placed on metallic glass forming systems where nucleation can occur both very near to the liquidus temperature or after substantial undercooling. The current state of the art of experimental research and modelling is surveyed in order to stimulate future investigations. The study of nucleation refers to the early stages of materials phase transformations in which a limited number of atoms or molecules are involved in the formation of seeds as a new phase originates from a matrix. Battezzati and Castellero (both: chemistry U. of Torino Italy) describe the theory of nucleation and discuss the thermophysical properties which mostly influence its rate. Although the material mostly focuses on classical theory starting from heterophase fluctuations other theories are also described. Also included is a detailed analysis of quantities related to solidification.