I am in a General Relativity class, and I am finding the usual tensor notation very difficult to think about -- it seems like there are too many names to express something simple. E.g., I think of the equation $X^\mu_\nu = \eta_{\nu\nu'}X^{\mu\nu'}$ something like this:
+---+ +---+
-| X |- = | X |-
+---+ | |----+-----+
+---+ | eta |
---+-----+
I don't know, it's just a sketch (and doesn't handle the punning of using indices to represent different bases, for example). But I'm interested in all alternatives; what notations are available to make tensors easier to think about?