Tensor Book Recommendation Request

Requirements

• Tensors
• Intuitive + Practical
• Reason for Tensor Introduction

Current Knowledge

• Course Notes
• Abstract + Theoretical

Solution 1:

Given the OP's background and interest in physics/engineering, I doubt most of these suggestions are good choices. If the OP has a decent math background, I would suggest Abraham, Marsden, and Ratiu's Manifolds, Tensor Analysis, and Applications. I do not personally know the following book, but try Tensor Analysis for Physicists by J.A. Schouten (in Dover); the author has a history in the subject :)

Solution 2:

The most intuitive exposition i have seen on the pure mathematical level is from Steven Roman's "Advanced Linear Algebra". This is still abstract, yet beautiful. A nice development of tensors in the applied mathematics level can be found in the book "Matrix Analysis for Scientists and Engineers" by Alan Laub. I also like very much the chapter on the tensor product from Atiyah and Macdonald "Introduction to Commutative Algebra"; this one is abstract but very concise and clear.