Explore the concept of geodesic complexity in Riemannian manifolds through this lecture from the Applied Algebraic Topology Network. Delve into the mathematical formalization of efficient robot motion planning, inspired by Farber's topological complexity. Examine recent work on complete Riemannian manifolds, focusing on the relationship between geodesic complexity and cut loci geometry. Learn about lower and upper bounds for geodesic complexity, and see these concepts applied through various examples. Gain insights into the technical challenges, structure of stratification, and open questions in this field of study.