Includes bibliographical references.

An introduction to additive combinatorics ; Elementary additive combinatorics ; Many additive quadruples ; An old new proof of Roth's theorem ; Bounds on exponential sums over small multiplicative subgroups ; Montreal notes on quadratic Fourier analysis ; Ergodic methods in additive combinatorics ; The ergodic and combinatorial approaches to Szemeredi's theorem ; Cardinality questions about sumsets ; Open problems in additive combinatorics ; Some problems related to sum-product theorems ; Lattice points on circles, squares in arithmetic progressions and sumsets of squares ; Problems in additive number theory. I ; Double and triple sums modulo a prime ; Additive properties of product sets in fields of prime order ; Many sets have more sums than differences ; Davenport's constant for groups of the form mathbb Z_3\oplus \mathbb Z_3\oplus \mathbb Z_3d ; Some combinatorial group invariants and their generalizations with weights