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This lecture, given by the instructor Malo Jézéquel, covers Möbius transformations in the context of SL(2, R). The lecture explores the properties of hyperbolic elements, fixed points, and the ping-pong lemma. It delves into the concept of bounded distortion and its implications, showcasing the factorization of Möbius transformations. The lecture concludes with a discussion on the Patterson-Sullivan measure and its role in understanding d-regularity. Throughout the lecture, various exercises are presented and solved to illustrate the theoretical concepts discussed.