I recently came across the existence of Penrose string diagram after curiously and naively researching the existence of index free notation for linear algebra. This seems to be a very interesting paper in the very same category of things I'd love to study and learn about but probably won't ever find the time!
You will possibly like Needham's "Visual Differential Geometry and Forms" and even if you don't have much time to study it, it's quite beautiful to look at from time to time.