On Learning Tensor Calculus I am highly intrigued in knowing what tensors are, but I don't really know where to start with respect to initiative and looking for an appropriate textbook.
I have taken differential equations, multivariable calculus, linear algebra, and plan to take topology next semester. Since Summer break is right at the corner, I was wondering if anyone would tell me if my mathematical background is able to handle tensor calculus, or if I need to know other subjects in order to be ready to learn about tensor. Any and all help would be appreciated.

Have a look at:  http://www.amazon.com/Einsteins-Theory-Introduction-Mathematically-Untrained/dp/1461407052/ref=sr_1_fkmr0_1?s=books&ie=UTF8&qid=1431089294&sr=1-1-fkmr0&keywords=relativity+theory+for+the+mathematically+unsohisticated
which is  Øyvind Grøn, Arne Næss:  Einstein's Theory: A Rigorous Introduction for the Mathematically Untrained
This is a serious book!  the second autho is (well, was  ...) a retired philosopher which required from the first author that everything in the book should be understandable for him, without a need of pencil and paper. Still it reaches some graduate level. By the way, the philosopher author was very famous, at least in Norway.
The first review on Amazon says:  "This is simply the clearest and gentlest introduction to the subject of relativity.
This is NOT a popular reading, it does get into the math but the introduction and pace is what sets this text apart.
The authors starts from baby steps and builds up the theory. The pace is easy and explanation are clear and the mathematical details are not left to the reader to figure out like in most text books.The physics is also explained very clearly
From an electronics engineering background and not having dealt with tensors before, this text help me bridge the gap and allows me to fully appreciate the machinery underlying this wonderful theory.I have tried reading Schultz,Lawden etc to understand the subject on my own but this text is a much better intro to the subject."  and other reviews are also very positive.
