This lecture discusses the solidification front stability, distinguishing between solidification in a plane front and in a pasty zone based on the distribution of liquid fraction. It covers the solidification modes, microstructures, and the stability criterion for solidification. The instructor explains the physical mechanisms involved in alloy solidification and the conditions leading to the formation of a supercooled zone. Additionally, the lecture explores the temperature profiles, liquidus temperature slope, and the impact of solute concentration on solidification stability.