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What is a good self study book in Differential Geometry. Keep in mind I won't have the advantage of being able to ask a professor any questions.

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    $\begingroup$ Ted Shifrin has a book which is free :alpha.math.uga.edu/~shifrin/ShifrinDiffGeo.pdf. I would suggest that you brush up on your multivariable calculus before reading it. That will make it much easier to go through. $\endgroup$ – Faraad Armwood Apr 27 '16 at 16:42
  • $\begingroup$ If you have access to Mathematica : "Modern Differential Geometry of Curves and Surfaces with Mathematica, Third Edition (Textbooks in Mathematics)" by Gray, Abbena, Salomon. It permits you to 1) see very appealing surfaces 2) more or less bypass some tedious computational aspect of many computations, even if some computations are very necessary to be done by hand... $\endgroup$ – Jean Marie Apr 27 '16 at 17:23
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The online notes on differential geometry by Balazs Csikos are really quite good for self-study: http://www.cs.elte.hu/geometry/csikos/ under Lecture Notes, then under BSM Lecture Notes. Assumed prerequisites are multivariate calculus, linear algebra, and just a little topology.

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