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I whish to understand the Tao green theorem but don't know where to start off. Which are some good texts that can give me knowledge to understand it and learn the knowledge surrounding it? Regards

Arman Sadeghi
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Asinomás
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The book by Tao 'Higher order Fourier analysis' (AMS, 2012) based on some of his lecture notes seems a very natural choice. The lecture notes themselves are available on his blog, I link to one of the posts as an example

The book does not give a complete proof though; I do not think there exists a book containing one.

Depending on what you know already you might however better start with the book by Tao and Vu 'Additive Combinatorics' for a more general introduction to the circle of ideas, including a proof of Szemerédi's theorem.

quid
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  • Additive combinatorics would be better if I knew less or more? – Asinomás Aug 18 '13 at 00:58
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    I rather meant if you knew less. At least if you knew less for the Additive Combinatorics side. But it could also depend on your particular background and interests. If you have a strong 'analysis' background you might prefer the former. Both are in part available n Tao's website so you could have a look and decide then. – quid Aug 18 '13 at 11:57
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    I just saw something on your background on another question. For really getting started in the subject I would recommend still something different see my answer to a question for a learning roadmap to Additive Combinatorics http://math.stackexchange.com/questions/454701/learning-roadmap-for-additive-combinatorics/454708#454708 – quid Aug 18 '13 at 12:22