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This lecture covers the meaning of derived functors in the context of extending modules, focusing on the extension of N by M. It explores the concept of Ext-modules, Yoneda extensions, and the significance of derived categories. The lecture delves into the process of deriving functors for left/right exact functors and provides an outlook on derived categories. It also discusses the derived category Ex(M,N) and the chain complex Hom(M,N) - Ext^i(M,N).