I have been dealing with tensors for quite a few years, working my way through a good number of different books on tensors. However, I keep getting frustrated at times at the low quality of many books. I have a good background in linear algebra and some real analysis, but I am not interested in tensors as a purely mathematical construct, but for applications in mechanics. What I am looking for would ideally include the following: - some modern notation and orientation towards linear algebra. Not just the old component-based approach, which seems more like an exercise in algebraic manipulation, without gaining any understanding - general tensors, not just Cartesian, ideally with some differential geometry applications - not geared primarily towards mathematicians, as my knowledge of analysis is not quite good enough. Rather oriented towards applied mathematicians, physicists, engineers, i.e. not an entire book just listing theorems and proofs (they have to be included to some extent, of course, but not making up 100% of the content) - perhaps some differential forms, but this is really not essential Does anyone know of a suitable book? Thanks.