Recently, essential progress has been made in the analysis of rapid solidification phenomena and their consequences for the formation of a largely unexpected "supersaturated grain-refined equiaxed microstructure". The highly undercooled rapid solidification is a non-equilibrium solidification which changes the growth velocity and solidification behavior, thus inducing that the as-solidified alloy granular grains are unstable because of the non-equilibrium effects. It is very important to investigate how to obtain the microstructures with higher stabilization to extend their application. Grain growth and thermal stability in single phase materials were discussed controversially, i.e., a kinetic one or a thermodynamic one. As for material preparation, non-equilibrium solidification and solid-state grain growth are two basic and correlated processes. So far, the above two fields have kept paces with the times and established relatively integrated systems, separately. In this book, the non-equilibrium liquid/solid transformation, solid-state grain growth and the interrelation between them were explored in combination with theoretical analyses.