Lectures on Analysis on Metric Spaces

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Focusing on the advancements in analysis within spaces lacking a smooth structure, this book delves into the behavior of Lipschitz functions and quasiconformal mappings. It presents a structured approach, beginning with fundamental covering theorems and progressing to Sobolev spaces applicable in broader contexts. The final sections introduce quasisymmetric maps in metric spaces. With a mix of classical and contemporary material, including exercises, it serves as an excellent resource for self-study or graduate courses in analysis and geometry.