Table of Contents

An introduction to additive combinatorics by A. Granville Elementary additive combinatorics by J. Solymosi Many additive quadruples by A. Balog An old new proof of Roth's theorem by E. Szemeredi Bounds on exponential sums over small multiplicative subgroups by P. Kurlberg Montreal notes on quadratic Fourier analysis by B. Green Ergodic methods in additive combinatorics by B. Kra The ergodic and combinatorial approaches to Szemeredi's theorem by T. Tao Cardinality questions about sumsets by I. Z. Ruzsa Open problems in additive combinatorics by E. S. Croot III and V. F. Lev Some problems related to sum-product theorems by M.-C. Chang Lattice points on circles, squares in arithmetic progressions and sumsets of squares by J. Cilleruelo and A. Granville Problems in additive number theory. I by M. B. Nathanson Double and triple sums modulo a prime by K. Gyarmati, S. Konyagin, and I. Z. Ruzsa Additive properties of product sets in fields of prime order by A. A. Glibichuk and S. V. Konyagin Many sets have more sums than differences by G. Martin and K. O'Bryant Devenport's constant for groups of the form $mathbb{Z}_3oplusmathbb{Z}_3oplusmathbb{Z}_{3d}$ by G. Browmik and J.-C. Schlage-Puchta Some combinatorial group invariants and their generalizations with weights by S. D. Adhikari, R. Balasubramanian, and P. Rath.