The concept of a principal G-bundle over a base space M is the mathematical foundation for the concept of a gauge field, where G is the gauged group and M is space or spacetime. This article reviews two ways of constructing principal G-bundles: one using quotients of groups, and one that starts with one principal bundle and constructs others over different base spaces using pullbacks. This is used to introduce the concept of a universal G-bundle, a principal G-bundle from which all other principal G-bundles may be constructed using pullbacks, at least in principle.
