Introduce geometric approaches to study dynamical control systems over manifolds. Cover fundamental control-theoretical results, such as controllability, observability, feedback stabilizability, symmetries and group actions, that are beyond linear control systems. Establish connections between control theory and mathematics, especially topology, differential geometry, Lie groups and Lie algebras. Final project focuses on engineering applications related to students� own research interests. Recommended prerequisites: a solid foundation in Linear Algebra and ECEN 4138/5138 and ECEN 5448. Same as MCEN 5488.