I am trying to read Tao's *Higher order Fourier analysis* but I would be very happy to find another book on the subject. I would like to learn something about the Gowers norm and about Roth's theorem (density increment and energy increment arguments). Sorry if this question is a bit too open ended . Lecture notes, even separately on each topic I just mentioned are absolutely fine. 


Part of the reason is that I am not sure what the natural context for Fourier measurability and complexity is, whatever natural means and I was hoping I could understand these if I had another reference. Thanks!



Another reference for higher order Fourier analysis
You could try "Nilpotent structures in Ergodic theory" by Host and Kra, which covers this topic in greater depth. 


