Updates of Serge Lang — Differential manifolds

It sounds like you have the version of this book from 1971. It was updated in the 1990s and can be found with the title "Differential and Riemannian Manifolds".


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

  1. John Lee, Introduction to Smooth Manifolds
  2. Loring Tu, An Introduction to Manifolds
  3. Guillemin and Pollack, Differential Topology
  4. Milnor, Topology from the Differential Viewpoint
  5. Do Carmo, Riemannian Geometry
  6. Bott and Tu, Differential Forms in Algebraic Topology
  7. Milnor, Morse Theory

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

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Book Recommendation

Differential Geometry

Manifolds

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