In many areas of mathematics, science and engineering, from computer graphics to inverse methods to signal processing, it is necessary to estimate parameters, usually multi-dimensional, by approximation and interpolation. Radial basis functions are a modern and powerful tool which work well in very general circumstances, and so are becoming of widespread use, as the limitations of other methods, such as least-squares, polynomial interpolation or wavelet-based, become apparent. This is the first book devoted to the subject and the author's aim is to give a thorough treatment from both the theoretical and practical implementation viewpoints. For example, he emphasises the many positive features of radial basis functions such as the unique solvability of the interpolation problem, the computation of interpolants, their smoothness and convergence, and provides a careful classification of the radial basis functions into types that have different convergence. A comprehensive bibliography rounds off what will prove a very valuable work.