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Introduction; 1. One century of logarithmic forms G. Wüstholz; 2. Report on p-adic logarithmic forms Kunrun Yui; 3. Recent progress on linear forms in elliptic logarithms Sinnou David and Noriko Hirata-Kohno; 4. Solving Diophantine equations by Baker’s theory Kálmán Györy; 5. Baker’s method and modular curves Yuri F. Bilu; 6. Application of the André–Oort conjecture Paula B. Cohen and Gisbert Wüstholz; 7. Regular dessins Jürgen Wolfart; 8. Maass cusp forms with integer coefficients Peter Sarnak; 9. Modular forms, elliptic curves and the ABC-conjecture Dorian Goldfeld; 10. On the algebraic independence of numbers Yu. V. Nesterenko; 11. Ideal lattices Eva Bayer-Fluckiger; 12. Integral points and Mordell–Weil lattices Tetsuji Shioda; 13. Forty years of effective results in Diophantine theory Enrico Bombieri; 14. Points on subvarieties of tori Jan-Hendrik Evertse; 15. A new application of Diophantine approximations G. Faltings; 16. Search bounds for Diophantine equations D. W. Masser; 17. Regular systems and ubiquity V. V. Beresnevich, V. I. Bernik and M. M. Dodson; 18. Diophantine approximation, lattices and flows Gregory Margulis; 19. Baker’s constant and Vinogradov’s bound Ming-Chit Liu and Tianze Wang; 20. Powers in arithmetic progression T. N. Shorey; 21. Greatest common divisor A. Schinzel; 22. Heilbronn’s exponential sum and transcendence theory D. R. Heath-Brown.

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