Geometric Algebra for Physicists : https://www.amazon.com/Geometric-Algebra-Physicists-Chris-Do...

Although not a small amount of effort, it really helps to learn geometric algebra notation:

http://www.amazon.com/Geometric-Algebra-Physicists-Chris-Dor...

Once you get an intuitive grasp of bivectors, it's not hard to "see" tensors as a linear map of bivector into bivector.

If you enjoy playing around with quaternions, you may also have fun with geometric algebra.

Geometric Algebra for Physicists is very clear and gently paced. http://www.amazon.com/Geometric-Algebra-Physicists-Chris-Dor...

This one also looks good: http://www.amazon.com/Linear-Geometric-Algebra-Alan-Macdonal...