If you want to understand Peluse's paper, I think the most directly relevant background reading would be Tao and Vu's Additive Combinatorics. Dummit and Foote'

If you want to understand Peluse's paper, I think the most directly relevant background reading would be Tao and Vu's Additive Combinatorics. Dummit and Foote's Abstract Algebra is an excellent book -- even if not very directly relevant to additive combinatorics. Analysis background would be useful, such as to be found in Stein and Shakarchi's series. Some introductory combinatorics would also be good (e.g. Stanley's Enumerative Combinatorics, or Van Lint and Wilson). Finally, analytic number theory would also be good to learn. For example, you might read Davenport's Multiplicative Number Theory. (Especially if you want to see integrals come into the picture.)