Master Tensor Calculus with Our Introductory Tensors Book

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So the tensor calculus part of my into to GR class is kicking my butt. I'm using the book by D'Inverno, but I feel like he's going too quickly over tensor calculus. Is there a more introductory text on tensors that I missed out on?

I've taken courses on linear algebra before, but not differential geometry. I feel like there's a huge gap between the two and was looking for something to bridge it.
 
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Sean Carroll's book is pretty good for this.
 
some differential geometry books treat this early, like the books by seth warner and noel j hicks. but the treatment by spivak in vol 2 os his big set is more detailed and explains the translation from classical (upper and lower indices) to modern (conceptual, multilinear) notation.