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.