In the next few days I will be posting a series of lectures about Einstein manifolds which is based on the book Einstein manifold by the group Arthur Besse

The course will cover the following material: Linear connections on vector bundles, Geodesics, Jacobi fields, Riemannian manifolds, Levi-Civita connection, Normal coordinates, Riemannian distance function, Sectional curvature, Ricci curvature, Scalar curvature, Lie groups, Kahler manifolds and Calabi-Yau theorem, Quaternion Kahler manifolds.