Pavel Grinfield is writing a number of tensor textbooks that he is self-publishing. They can be found for free on his website [1]. He also has Youtube channel with some great videos. I just started supporting him on Patreon as I think he has a really great teaching style.

I have no relationship to Pavel and just want to support his efforts.

[1] https://grinfeld.org/

I have his book and others relating to tensor analysis and its good as is his YouTube channel, if anyone is after a gentler introduction to differential geometry I've recently discovered this book "Curvature of Space and Time, with an Introduction to Geometric Analysis" by Iva Stavrov. It glosses over and leaves out a lot of the proofs and topology discussions etc and gives a good overview to get started.

Edit: a link https://smile.amazon.com/Curvature-Introduction-Geometric-An...

Pretty nice overview, I'd highly recommend Hartl's gravity for a physics focused introduction to tensor calculus along with an actual application centric usage of the same: https://www.amazon.com/Gravity-Introduction-Einsteins-Genera...

I dunno why there is so much interest in this subject. Just knowing basic calculus and linear algebra will cover the majority of applications. Why does the chapter on matrix multiplication come 7 chapters after "The Christoffel Symbol". I think there are better guides than this, shorter and more to the point and better organized. Start with Cartesian tensors and polar coordinate transforms.

It would be cool to have some kind of PDF export! Definitely seems very educational nevertheless.

Need more examples in the beginning of why tensors. The Euler example is good but not clear. But overall at least the introduction is good.

The content seems good but it's hard to get used to the pompous style.