It sounds like you're looking for a about Tensor Calculus by J.L. Synge and A. Schild — likely to share on a forum, social media, or study group.
The deep insight: A tensor is not a grid of numbers. A tensor is a geometric object living on a manifold. Coordinates are just temporary scaffolding. tensor calculus synge pdf
Why does this matter? Because general relativity and differential geometry become clearer once you stop asking “How does this component transform?” and start asking “What is this tensor doing ?” It sounds like you're looking for a about