I have studied from baby Do Carmo (Differential Geometry of Curves and Surfaces) and have a background in pointset topology. What is the next best book to use? I'm looking for a good diff geo book to independent study from next semester. My professor recommended Introduction to Differentiable Manifolds and Lie Groups by Frank Warner, but it seems really advanced: http://www.amazon.com/Foundations-D...bs_sr_3?ie=UTF8&s=books&qid=1207587941&sr=1-3 along with Comparison Theorems by Ebin and Cheeger (yet to be published, but will be published before next semester). I was thinking about Do Carmo's Riemannian Geometry, but I'm not sure. There does not seem to be such a clear lineage when it comes to differential geometry books.