Explore the symplectic geometry of Teichmueller spaces for surfaces with boundary in this 51-minute lecture delivered by Eckhard Meinrenken from the University of Toronto. Presented on December 6, 2023, as part of the Workshop on Operator Algebras and Applications: Non-Commutative Geometry at the Fields Institute, this talk delves into advanced mathematical concepts. Gain insights into the intersection of symplectic geometry and Teichmueller theory, focusing on surfaces with boundary. The lecture is a component of the broader Thematic Program on Operator Algebras and Applications, offering a deep dive into this specialized area of mathematics.