(ie. current pure mathematics inspired by / from "gauge (field) theory" in physics)

If I'm not mistaken "gauge field" in physics is equivalent to "connections on vector bundles" in maths. - In the context of your comment, I mean 'gauge theory' in the context of maths.

@Paul: "... there is a well-known narrative which explains the passage from single variable calculus over C to the theory of Riemann surfaces. It is often described in basic complex analysis / algebraic geometry courses." -- Some references? - Regards

@Andy: @quid: Ok. Thanks for the responses. - Sadiq @Paul: ok. This is very useful. Thank you. - Sadiq

This is more of a technical book. I was searching for an outline-type response.