This volume contains 21 research and survey papers on recent developments in the field of diophantine approximation, which are based on lectures given at a conference at the Erwin Schr dinger-Institute (Vienna, 2003). The articles are either in the spirit of more classical diophantine analysis or of a geometric or combinatorial flavor. Several articles deal with estimates for the number of solutions of diophantine equations as well as with congruences and polynomials.

This volume contains 21 research and survey papers on recent developments in the field of diophantine approximation, which are based on lectures given at a conference at the Erwin Schrodinger-Institute (Vienna, 2003). The articles are either in the spirit of more classical diophantine analysis or of a geometric or combinatorial flavor. Several articles deal with estimates for the number of solutions of diophantine equations as well as with congruences and polynomials.

The C.I.M.E. session in Diophantine Approximation, held in Cetraro (Italy) June 28 - July 6, 2000 focused on height theory, linear independence and transcendence in group varieties, Baker's method, approximations to algebraic numbers and applications to polynomial-exponential diophantine equations and to diophantine theory of linear recurrences. Very fine lectures by D. Masser, Y. Nesterenko, H.-P. Schlickewei, W.M. Schmidt and M. Walsschmidt have resulted giving a good overview of these topics, and describing central results, both classical and recent, emphasizing the new methods and ideas of the proofs rather than the details. They are addressed to a wide audience and do not require any prior specific knowledge.

The 15 papers of this selection of contributions to the Journ es Arithm tiques 1987 include both survey articles and original research papers and represent a cross-section of topics such as Abelian varieties, algebraic integers, arithmetic algebraic geometry, additive number theory, computational number theory, exponential sums, modular forms, transcendence and Diophantine approximation, uniform distribution.