# Differential Geometry Control Systems

Victor Ayala
In this talk, we present the main ingredients of the Control Systems Theory from the Differential Geometry point of view. After that, we concentrate our attention on the class $Σ$ of Linear Control Systems on Lie Groups, and its connections with Almost Riemannian Geometry. We mention some recent results on the controllability property and the existence, uniqueness and the shape of control sets of $Σ$.