This volume contains the contributions of the International Dortmund Meeting on Approximation Theory (IDoMAT 95) at Haus Bommerholz the conference center of Dortmund University during the week of March 13-17, 1995. At this international conference researchers and specialists from China, England, France, Hungary, Israel, Italy, Romania, U.S.A. and Germany described new developments in the fields of approximation theory. The authors discuss a variety of important ideas, questions and applicable methods in applied sciences and in several fields of approximation theory which lead to new challenges to the approximation by means of linear operators and shape preserving approximation, methods for the study of differential (diffusion) equations, approximation results of solutions of specific hyperbolic differential equations, polynomial and spline interpolation, density problems in multivariate approximation, orthogonal polynomials and wavelets. This volume collects the complete papers of the invited lectures together with a selection of papers relating to the research talks presented at IDoMAT 95.