Explore Riemannian manifolds, isometries, and geodesics in this 55-minute lecture by Nikolay Bogachev from the University of Toronto. Delve into the upper half-plane with hyperbolic metric as part of the "Geometry, Arithmetic, and Dynamics of Discrete Groups" series at the Fields Institute. Gain insights into advanced mathematical concepts through this graduate-level presentation, offered as part of the Shared Graduate Courses Program on September 17, 2024.