Abstract: Additive combinatorics provides a powerful framework for understanding additive structure in finite-rank abelian groups. I’ll give an overview of a few of the main techniques in this field, focusing on the structure/randomness dichotomy pioneered by Szemerédi and Gowers. Along the way, I’ll also introduce a close connection between additive combinatorics and ergodic theory, and explain how the transference principle developed by Green and Tao allows additive combinatorics to be applied to questions of additive structure in the set of prime numbers.