Does anyone know of any good references for physical examples of gauge theory (as a mathematically precise theory of connection on principal bundles). Simple examples will do (e.g the $U(1)$ electromagnetic theory), for someone who has just started learning about principal bundles, and has little/no background in physics. An introduction to "Yang-Mills" theory would also be nice. What I really want is something to connect what mathematicians call "gauge theory" and what physicists call "gauge theory" (starting from the maths point of view).
I would also like references for physical examples of spin geometry. Again, in a mathematical style in the context of clifford and spin bundles (over spacetime manifold). Thanks.