My favorite reference talking about tensors is applied to modeling and simulation of space vehicles, "Modeling and Simulation of Aerospace Vehicle Dynamics"
The point of all this is summed up nicely in above textbook, "We will use tensors to model vehicle dynamics, independent of coordinate systems."
If you can use amazon search within a book read the first 2 chapters of the book and hopefully this will give you a nice introduction. (note just search by page number, like 1 then 4, 8, etc.)