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This lecture covers the metallurgical processes of hardening and maturation in metals and alloys, focusing on the formation of martensite, the role of alloying elements, and the effects of heat treatment. It discusses the concepts of hardenability, tempering, and the transformation of microstructures during cooling and heating cycles. The instructor presents examples of phase diagrams, TTT diagrams, and TRC diagrams to illustrate the evolution of microstructures in different steel compositions. Additionally, the lecture explores the impact of secondary hardening, the tempering of martensite, and the influence of alloy elements on the properties of hardened steels.