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This lecture covers the CW Approximation Theorem and the construction of Postnikov towers, starting with the definition of weak equivalence and its implications for homotopy groups. The instructor explains the process of constructing a CW complex from a given space, ensuring isomorphism and bijection on homology groups. The lecture delves into the detailed steps of the CW Approximation Theorem, including the induction process and the construction of maps between spaces. The instructor emphasizes the importance of making choices in the construction process and highlights the significance of working with CW complexes due to their structured cell composition.