An introduction to differential geometry - Amur, K. S. (Krishna S.) (Alpha Science International, 2010)
"The concept of a differentiable manifold is introduced in a simple manner without going into its topological structure. Subsequently the reader is led to the same conceptual details as are found in other texts on the subjects. Since calculus on a differentiable manifold is done via the calculus on Rn, a preliminary chapter on the calculus on Rn is added. While introducing concepts such as tangent and cotangent bundles, tensor algebra and calculus, Riemannian geometry etc., enough care is taken to provide many details which enable the reader to grasp them easily."--Publisher's description