We give a self-contained exposition of selected results in additive
combinatorics over the group {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 efficiently ... more >>>