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This lecture delves into the local structure of totally disconnected locally compact groups, focusing on commensurated subgroups, completions, and local automorphisms. The instructor discusses the Schlichting and Belyaev completions, the induced topology, and the quasi-centre of these groups. The lecture also covers the local adjoint of a group, the concept of local isomorphisms, and the uniqueness of local automorphisms. Additionally, the instructor explores the universality of these groups and the properties of local homomorphisms, local isomorphisms, and local isomorphism classes.