For than a half century, Mats Hillert has contributed greatly to the Science of Materials He is widely known and respected as an innovator and an educator, a scientist with an enormous breadth of interest and depth of insight The difficult choice of twenty four papers from a publication list of than three hundred was carried out in consultation with him He also suggested or approved names of those scientists who would be invited to write brief introductions to each of the papers A brief reading of the topics of the selected papers and their introductions reveals something of their range and depth Several early selections including internal reports of the Swedish Institute for Metal Research, published here in their original shape contained seminal material that established Mats as a leading figure in the study of phase transformations in solids Others established his presence in the areas of solidification and computational thermodynamics This volume represents a judicious sampling only of Mats Hillert s extensive body of work it is necessarily incomplete, but it is hoped and expected that it will prove useful to students of Materials Science and Engineering at ail levels, and that it will inspire the further study and appreciation of his many contributions John Aqren is professor in Physical Metallurgy at KTH in Sweden and a member of the Royal Swedish Academy for Engineering Sciences His research interests are in thermodynamics, kinetics of phase transformations and microstructural evolution in steels and other alloys.Yves Brechet is Professer of Materials Science at the Institut National Polytechnique de Grenoble INPG and at the Institut Universitaire de France IUF His research interests are in diffusive phase transformations, microstructure evolution and mechanical properties Christopher Hutchinson is University Fellow with the Department of Materials Engineering, Monash University, Melbourne, Australia His work concerns the coupling of phase transformations and plasticity in the design of steels, AI and gq based alloys Jean Philibert, now retired, was professer of Materials Science His research covers metallurgy and ceramics His studios on diffusion lead him to publish two text books, La Diffusion dans les Solides with Yves Adda and later Atom Movements, Diffusion and Mass Transport in Solids Gary Purdy is University Professor, Department of Materials Science and Engineering, McMaster University, Hamilton, Ontario Canada His research interests include the Thermodynamics and Kinetics of Phase Transformations and their role in microstructure development Computational Thermodynamics Calculation of Phase Calculation of phase diagrams using the CALPHAD approach General information about the fields of computational thermodynamics and computational kinetics The developers and the end uses of Thermo Calc, DICTRA, JMatPro, FactSage, Pandat, and MTDATA are invited to submit articles and or examples that are preferably focused on how to 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