W. W. L. Chen is Emeritus Professor of Mathematics in the Department of Mathematics at Macquarie University, Sydney. W. T. Gowers is Rouse Ball Professor of Mathematics in the Department of Pure Mathematics and Mathematical Statistics (DPMMS) at the University of Cambridge. H. Halberstam is Professor Emeritus in the Department of Mathematics at the University of Illinois, Urbana-Champaign. W. M. Schmidt is a Distinguished Professor Emeritus in the Department of Mathematics at the University of Colorado, Boulder. R. C. Vaughan is Professor of Mathematics in the Department of Mathematics at Pennsylvania State University.

• Preface; Acknowledgments; Klaus Roth at 80; Numbers with a large prime factor II Roger Baker and Glyn Harman; Character sums with Beatty sequences on Burgess-type intervals William D. Banks and Igor E. Shparlinski; The Hales-Jewett number is exponential: game-theoretic consequences József Beck, Wesley Pegden and Sujith Vijay; Classical metric diophantine approximation revisited Victor Beresnevich, Vasily Bernik, Maurice Dodson and Sanju Velani; The sum-product phenomenon and some of its applications J. Bourgain; Integral points on cubic hypersurfaces T. D. Browning and D. R. Heath-Brown; Binary additive problems and the circle method, multiplicative sequences and convergent sieves Jörg Brüdern; On the convergents to algebraic numbers Yann Bugeaud; Complexity bounds via Roth's method of orthogonal functions Bernard Chazelle; Some of Roth's ideas in discrepancy theory William Chen and Giancarlo Travaglini; Congruences and ideals Harold G. Diamond and H. Halberstam; Elementary geometry of Hilbert spaces applied to abelian groups P. D. T. A. Elliott; New bounds for Szemerédi's theorem II: a new bound for r4(N) Ben Green and Terence Tao; One-sided discrepancy of linear hyperplanes in finite vector spaces Nils Hebbinghaus, Tomasz Schoen and Anand Srivastav; How small must ill-distributed sets be? H. A. Helfgott and A. Venkatesh; On the power-free values of polynomials in two variables C. Hooley; On a question of Browning and Heath-Brown Nicholas M. Katz; Good distribution of values of sparse polynomials modulo a prime Sergei Konyagin; Diophantine approximation and continued fractions in power series fields A. Lasjaunias; On transfer inequalities in diophantine approximation Michel Laurent; On exponential sums with multiplicative coefficients Helmut Maier; Multiplicative dependence of values of algebraic functions David Masser; Linear forms in logarithms, and simultaneous diophantine approximation Bernard de Mathan; The Caccetta-Häggkvist conjecture and additive number theory Melvyn B. Nathanson; L2 discrepancy and multivariate integration Erich Novak and Henryk Wózniakowski; Irregularities of sequences relative to long arithmetic progressions A. Sárközy and C. L. Stewart; The number of solutions of a linear homogeneous congruence II A. Schinzel, with an appendix by Jerzy Kaczorowski; The diophantine equation α1x1 . . . α1xn = f (x1,…,xn) Wolfgang M. Schmidt; Approximation exponents for function fields Dinesh S. Thakur; On generating functions in additive number theory I R. C. Vaughan; Words and transcendence Michel Waldschmidt; Roth's theorem, integral points and certain ramified covers of Ρ1 Umberto Zannier.