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This lecture by the instructor covers the topic of Testing General Relativity with Cosmology, focusing on the geometrical setup, modelling the world as a manifold, the curvature tensor, the metric, and the complete model. It delves into teleparallelism, coincident general relativity, and the extension to f(Q) gravity, including cosmology and black holes. The lecture explores the field equations of STEGR, the improved action principle, and the comparison between GR and teleparallel gravity. It also discusses the ansatz for cosmology in f(Q) and the study of black holes in this context.