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I am looking to learn about manifolds for use in signal processing. I have a engineering degree where I have covered calculus and basic linear algebra, with this background in mind, does anyone have a good recommendations for a introductory textbook on manifolds?

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Given the background you stated (calculus and linear algebra, an engineering degree; presumably no advanced calculus, no topology, no undergraduate differential geometry, etc.), I think a more appropriate place to begin than Spivak's Calculus on Manifold or Lee's Introduction to Smooth Manifolds (the two books thus far suggested) is Dodson/Poston's Tensor Geometry. After their book, and you can probably skip most of the physics relativity stuff in it, you will be in a better position to look at the other books suggested. – Dave L. Renfro Jan 9 '13 at 15:55

If you want an elementary introduction to manifolds, assuming very little background, I'd suggest you start with

Then (or else)
You might want to look into one or more of the following:

You might want to compare Lee's book (table of contents, etc) with

You can preview each of the texts linked above at to see which best meets your needs, in terms of topics covered, apparent level of difficulty, etc.

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Calculus on Manifolds by Spivak is a quality introduction if you haven't seen a lot of Analysis.

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