I am curious about which areas of mathematics one should be comfortable with before learning QFT. I am familiar with the "learn-it-as-you-go" approach often advocated in physics, but would like to know how to avoid that in learning QFT. Naming of specific textbooks is appreciated.

(For the sake of this discussion, "learning QFT" can be taken to mean "learning at the level of/from Peskin and Schroeder's text.")

In particular, I would like to know what, in addition to the material in Rudin's Real and Complex Analysis, one should know. Would this be sufficient? How about Folland's Real Analysis?

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    $\begingroup$ Listed inside that overarching Book recommendations list is a link to the question Textbook on group theory to be able to start qft which seems to be what you're looking for. $\endgroup$ – Kyle Kanos Sep 12 '14 at 2:04
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    $\begingroup$ Real and complex analysis will get you almost nowhere in QFT. You have to have, at the very least, a good idea of Hilbert spaces, operators, group theory, Lie algebras... and I am not even sure that gets you much past the introduction. $\endgroup$ – CuriousOne Sep 12 '14 at 2:12
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    $\begingroup$ @Optional: My last math class was over 30 years ago. If I remember correctly, the last math book I looked into was Choquet-Bruhat's "Analysis, manifolds and physics", and I don't think that's a good way to get started... $\endgroup$ – CuriousOne Sep 12 '14 at 5:09
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    $\begingroup$ @CuriousOne It really depends what you want to do with it - you can do scalar QFT perfectly fine without using any group theory, Lie algebras and the likes. I think some complex analysis is essential, since you must be able to perform contour integrals. $\endgroup$ – Danu Sep 12 '14 at 12:05
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    $\begingroup$ Cross-posted to math.stackexchange.com/q/928359/11127 $\endgroup$ – Qmechanic Sep 12 '14 at 12:25