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This lecture is the first in a series on Teichmüller theory presented by Federica Fanoni at the Centre International de Rencontres Mathématiques in Marseille, France. Explore the fundamental concepts of Teichmüller space through various interpretations, examining its topology, geometry, and boundary construction. Focus primarily on closed surfaces while gaining insights into the additional challenges presented by non-closed surfaces. The lecture was recorded during the thematic meeting "Geometric structures and discrete group actions" on April 14, 2025. Access this video and other mathematical talks on CIRM's Audiovisual Mathematics Library (http://library.cirm-math.fr), which offers helpful features like chapter markers, keywords, abstracts, bibliographies, and Mathematics Subject Classification for enhanced navigation and research.
