Updates of Serge Lang — Differential manifolds I have Serge Lang — differential manifolds. An interesting read. But the book is 50 years old. Are there newer books that give a better and more comprehensive treatment of the material, or this the best of its kind?

I don't have much experience with Lang's book, but some other books that are in vogue amongst graduate students right now are:

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*John Lee, Introduction to Smooth Manifolds

*Loring Tu, An Introduction to Manifolds

*Guillemin and Pollack, Differential Topology

*Milnor, Topology from the Differential Viewpoint

*Do Carmo, Riemannian Geometry

*Bott and Tu, Differential Forms in Algebraic Topology

*Milnor, Morse Theory
The first four are of a more introductory nature, while the last three draw on material from the first four.
