On the Mathematics of the Berry Phase

I tried to upload this to my wordpress however it wasn’t working.
So here is a link to a pdf file of some notes and observations I wrote over the course of a few years on the Geometric Phase.
Mathematics of the Geometric Phase by no means is this original, and there are many excellent textbooks and review articles out there. Including http://www.amazon.com/Geometric-Phase-Quantum-Systems-Mathematical/dp/3540000313 and This textbook. Most of this article is liberally borrowed and influenced from the following source Y Ben Aryeh Review article.