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 Schrödinger-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.

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-Dedication to Wolfgang Tichy.-Schäffer´s Determinant Argument.-Arithmetic progressions and Tic-Tac-Toe games.-Metric discrepancy results for sequences {NkX } and Diophantine equations.-Mahler´s classification of numbers compared with Kosma´s, II.-Rational approximations to a q-analogue of p and some other q-series.-Orthogonality and digit shifts in the classical Mean Squares problem in irregularities of point distribution.-Applications of the Subspace Theorem to certain Diophantine problems.-A generalization of the Subspace Theorem with polynomials of higher degree.-On the Diophantine equation Gn (x) = Gm (y) with Q(x,y) = 0.-A criterion for polynomials to divide infinitely many k-nomials.-Approximants de Pade des q-Polylogarithmes.-The set of solutions of some equation for linear recurrence sequences.-Counting algebraic numbers with large height I.-Class number conditions for the diagonal case of the equation of Nagell-Ljunggren.-Construction of approximations to zeta-values.-Quelques aspects Diophantiens des varietes Toriques Projectives.-Une inegalite de Lojasiewicz arithmetique.-On the continued fraction expansion of a class of numbers.-The number of solutions of a linear homogeneous congruence.-A note on Lyapunov theory for Brun algorithm.-Orbit sums and modular vector invariants.-New irrationality results for dologarithms of rational numbers.