  These notes arose from my Cambridge Part III course on Additive
Combinatorics, given in Lent Term 2009. The aim was to understand the simplest
proof of the Bourgain-Glibichuk-Konyagin bounds for exponential sums over
subgroups. As a byproduct one obtains a clean proof of the Bourgain-Katz-Tao
theorem on the sum-product phenomenon in F_p. The arguments are essentially
extracted from a paper of Bourgain, and I benefitted very much from being in
receipt of unpublished course notes of Elon Lindenstrauss. No originality is
claimed.
