This volume presents the main results of the 4th International Conference on Multivariate Approximation, which was held at Witten-Bommerholz, September 24-29, 2000. Nineteen selected, peer-reviewed contributions cover recent topics in constructive approximation on varieties, approximation by solutions of partial differential equations, application of Riesz bases and frames, multiwavelets and subdivision. The book is an essential resource for researchers and graduates in applied mathematics, computer science and geophysics who are interested in the state-of-the-art developments in multivariate approximation.