"This collection gives an integrated picture on main streams in contemporary number theory. As such, it can be recommended to active number theorists and also to a general mathematical audience." -EMS Newsletter, December 2003

• Preface -- Completeness Problems and the Riemann Hypothesis: An Annotated Bibliography/Michel Balazard -- A Survey on Pure and Mixed Exponential Sums Modulo Prime Powers/Todd Cochrane and Zhiyong Zheng -- One Hundred Years of Normal Numbers/Glyn Harman -- On Theorems of Barban-Davenport-Halberstam Type/C. Hooley -- Integer Points, Exponential Sums and the Riemann Zeta Function/?. N. Huxley -- Recent Developments in Automorphic Forms and Applications/Wen-Ching Winnie Li -- Convergence of Corresponding Continued Fractions/Lisa Lorentzen -- On the Analytic Continuation of Various Multiple Zeta-Functions/Kohji Matsumoto -- Quelques Remarques sur la Theorie d’lwasawa des Courbes Elliptiques/Bernadette Perrin-Riou -- Computing Rational Points on Curves/Bjorn Poonen -- G. H. Hardy As I Knew Him/Robert A. Rankin -- Some Applications of Diophantine Approximation/R. Tijdeman -- Waring’s Problem: A Survey/R. C. Vaughan and T. D. Wooley -- Solving the Pell Equation/H C. Williams.