This course consists of two parts.
The first part is "Analysis on Manifolds", starting from the definition a differentiable manifold, vectors fields, differential forms, integration, Stokes theorem.
The second part is "Curvature" and it focuses on Riemannian manifolds and submanifolds of Euclidean space: Riemannian metric, parallel transport, connections, geodesics, curvature, isoperimetric inequalities.