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As seen in previous questions, I'm interested in gauge theory, although I have no idea how to do any of the mathematics, though i'd like to start. With that in mind, Are there any good sources that start at the basics?

As an aside, I've tried to decipher it through Wikipedia, although the rabbit holes required for all the terminology is long and dense, though this sentence is basically irrelevant.

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  • $\begingroup$ It will be quite hard to give truly useful answers to this without an understanding of where you stand in terms of prerequisites. $\endgroup$
    – Emilio Pisanty
    May 19 at 16:43
  • $\begingroup$ This answer reviews many ressources on group theory for physicists. The other answers there may also be relevant. $\endgroup$
    – SolubleFish
    May 19 at 16:46
  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/6108/2451 , physics.stackexchange.com/q/344940/2451 , physics.stackexchange.com/q/214966/2451 and links therein. $\endgroup$
    – Qmechanic ♦
    May 19 at 16:47
  • $\begingroup$ I'm effectively a nobody in high school, junior year. Been looking into this stuff for years, and I want to start actually understanding it. $\endgroup$
    – Quinn Jackson
    May 19 at 16:56
  • $\begingroup$ These lectures are a nearly self-contained overview of the mathematics underlying the topics you ask about. They start from the fundamental mathematics of logic and set theory before embarking on a journey that ends with quite sophisticated differential geometry. The lectures are long and sometimes quite dense, but if you start at the beginning and understand each lecture in sequence, then by the end you will have all the tools you need. If you have very little background that might take years, but the information is there. $\endgroup$
    – J. Murray
    May 19 at 18:48

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Any “Mathematics for Physicists” at the suitable level will have an introduction to these things. In addition, most QFT books at the graduate level should have self contained introductions to these topics.

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