Explore the symplectic geometry of Teichmueller spaces for surfaces with boundary in this 57-minute lecture delivered by Eckhard Meinrenken from the University of Toronto. Presented on December 7, 2023, as part of the Fields Institute's Workshop on Operator Algebras and Applications: Non-Commutative Geometry, this talk delves into advanced mathematical concepts within the broader context of the Thematic Program on Operator Algebras and Applications. Gain insights into the intricate relationships between symplectic geometry and Teichmueller spaces, focusing specifically on surfaces with boundary. Enhance your understanding of this specialized topic in mathematics and its applications in operator algebras and non-commutative geometry.