Reddit reviews Elementary Primer For Gauge Theory, An

Here is a cute article by Terrence Tao on gauges:

https://terrytao.wordpress.com/2008/09/27/what-is-a-gauge/

A gauge transformation is essentially a change of coordinates which is usually done to simplify whatever problem you are trying to solve. These "coordinates" aren't your usual x, y, and z, but something a bit more abstract, but still can be understood geometrically. I find it unfortunate that E&M textbooks don't discuss the geometry of gauges... I like "An Elementary Primer for Gauge Theory" by Moriyasu:

https://www.amazon.com/Elementary-Primer-Gauge-Theory-Moriyasu/dp/9971950944