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Notes on differential geometry, (Van Nostrand mathematical studies)

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First, the binding: It's paperback.

This was Hicks' only book - he died young. It's a great concise intoduction to differential geometry, sort of the Schaum's Outline version of Spivak's epic "A Comprehensive Introduction to Differential Geometry" (beware any math book with the word "Introduction" in the title - it's probably a great book, but probably far from an introduction.) The ten chapters of Hicks' book contain most of the mathematics that has become the standard background for not only differential geometry, but also much of modern theoretical physics and cosmology. It thus makes a great reference book for anyone working in any of these fields. Make sure that you do, or at least read, all of the exercises - they're an important part of the book. The only caveat I have is that Hicks wasn't kidding when he included the word "Notes" in the title - as I said, the book is concise.