For the reader with a basic knowledge of the definition of tangent space on a manifold (chapter zero) this book is excellent. I find it one of the true masterpieces of pedagogy among the books I've read. It's a clear exposition of differential geometry from the mathematical standpoint. I think it goes well with hirsch's differential topology and it's always good to get a second perspective on Diff.G from the physics point of view, like Weinberg's Gravitation and Cosmology.