Pmb, I've edited your post to be a question, since we're trying to be better at enforcing our "posts must be phrased as questions rule." If you'd prefer a different title, please do feel free to change it!

I think you'll get little response because tensor notation isn't commonly taught until upper level mathematics or physics courses, and we don't have a lot of folks who have had that kind of training. I have learned a bit of it, and I know of two types of tensor notation. The common one (that I learned in upper level coursework) is the index notation used in Ricci calculus. I won't go into descriptions because I'd probably get some of it wrong at this point (I rarely use it), and there's already a nice description at Mathworld:

http://mathworld.wolfram.com/Tensor.html(As an aside, I'd highly recommend Mathworld to anyone needing a good mathematics resource but not wanting to shell out money for a physical book.)

The less common one (that I learned of in

*The Road to Reality* by Roger Penrose rather than in school) is Penrose's graphical notation. It seems to be notable enough to get cited on Wikipedia (but not on Mathworld):

http://en.wikipedia.org/wiki/Penrose_graphical_notation