this volume contains a selection of eighteen peer-reviewed articles that were presented at the 5th international conference on multivariate approximation, held in witten-bommerholz in september 2002. the contributions cover recent developments of constructive approximation on manifolds, approximation by splines and kernels, subdivision techniques and wavelet methods. the main topics are:- applications of multivariate approximation in finance- approximation and stable reconstruction of images, data reduction- multivariate splines for lagrange interpolation and quasi-interpolation- radial basis functions- spherical point sets- refinable function vectors and non-stationary subdivision- applications of adaptive wavelet methods- blending functions and cubature formulae- singularities of harmonic functionsthe book provides an overview of state-of-the-art developments in a highly relevant field of applied mathematics, with many links to computer science and geophysics.