Book Abstract: This meticulously edited selection of papers comes out of the Ninth International Symposium on Approximation Theory held in Nashville, Tennessee, in January, 1998. Each volume contains several invited survey papers written by experts in the field, along with contributed research papers. This book should be of great interest to mathematicians, engineers, and computer scientists working in approximation theory, wavelets, computer-aided geometric design (CAGD), and numerical analysis. Among the topics included in the books are the following: adaptive approximation approximation by harmonic functions approximation by radial basis functions approximation by ridge functions approximation in the complex plane Bernstein polynomials bivariate splines constructions of multiresolution analyses convex approximation frames and frame bases Fourier methods generalized moduli of smoothness interpolation and approximation by splines on triangulations multiwavelet bases neural networks nonlinear approximation quadrature and cubature rational approximation refinable functions subdivision schemes thin plate splines wavelets and wavelet systems