This lecture by the instructor covers the local structure of totally disconnected locally compact groups, focusing on the properties of GER and Mon (G). The lecture discusses the regionally expansive nature of Mon (G) and its faithful action on a CA graph. Theorem 4.2 states that if G is GER, then G is CA-simple. The lecture also delves into Theorem 4.6, which explores the quotient G-space of G(LU(G)), emphasizing the faithful action of G and the minimality of Mon (G). Various proofs and facts are presented throughout the lecture, shedding light on the intricate properties of these groups.