I am going to be entering the university of texas graduate physics department in August. I am currently signed up for the class "Topics in Geometry and Quantum Physics" (http://www.ma.utexas.edu/users/dafr/M392C/index.html) and am pretty worried about the summer reading. I am having a hard time with Spivak's "Comprehensive Introduction to Differential Geometry." Well, I am able to read the material (after a lot of thought/concentration) but still am unable to solve any problems. I was wondering if anyone had any good, more basic recommendations for learning differential geometry. Furthermore, should I be spending time trying to answer the problems, or should I just read the text? I hope this class won't be too far over my head. Thanks in advance.