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This lecture covers the concept of interpolation spaces in Banach spaces, focusing on the interpolation couple of two real (complex) Banach spaces. It explains the conditions for a vector subspace of V to be an interpolation couple, along with the max and inf operations. The lecture also discusses the properties of interpolation spaces between X and Y, emphasizing the K-method and real continuous interpolation spaces. Various examples and mathematical operations are presented to illustrate the theory.