In 1953, Roth proved that a set in ${1, \dots,N} containing no non trivial arithmetic progressions of length three has size at most $O(N/log(log(N))$ using Fourier analysis. Although his method does not directly apply to longer arithmetic progressions, Roth’s proof features interesting connections between Fourier analysis and the additive structure of a set. To illustrate this, I will give some elements of the proof in the finite field setting.