 Chapter 1: Manifolds (definition, examples,
diffeomorphisms, constructing manifolds, theorem of Sard
partition of Unity, Whitney's embedding theorem,
Brower's fixed point theorem)
 Chapter 2: Tensor analysis (general tensors,
antisymmetric tensors, tangent space and tensor fields,
exterior derivative, integration on manifolds, chains and
boundaries, theorem of Stokes for chains, Theorem of Stokes
for oritented manifolds)
 Chapter 3: Riemannian geometry (metric tensors, Hodge star
operation, Riemannian manifolds, Theorem of Stokes for Riemannian
manifolds, connections, covariant derivative, parallel transport,
geodesics, Riemannian curvature, Ricci tensor and scalar curvature,
the second Bianchi identity, General relativity).
