We give a self-contained exposition of selected results in additive combinatorics over the group GF (2)n = {0, 1}n. In particular, we prove the celebrated theorems known as the Balog-Szemeredi-Gowers theorem (’94 and ’98) and the Freiman-Ruzsa theorem (’73 and ’99), leading to the remarkable result by Samorodnitsky (’07) that linear transformations are… (More)