Explore the concept of Young towers for geodesic flows on specific non-positively curved surfaces in this comprehensive lecture by Carlos Matheus from CNRS, France. Delve into the history, key results, and theoretical foundations of this mathematical topic. Gain insights into Jacobi fields, the churn of axioms, and the intricacies of hyperbolic maps. Examine the cross-section notation and relevant theorems that contribute to understanding this complex subject within the field of differential geometry and dynamical systems.