Title: An Introduction to the Radial Basis Function Method The radial basis function (RBF) method is a primary tool for interpolating multidimensional scattered data. The methods' ability to handle arbitrarily scattered data, to easily generalize to several space dimensions, and to provide spectral accuracy have made it particularly popular in several different types of applications. Some of the more recent of these applications include cartography, neural networks, medical imaging, and the numerical solution of partial differential equations (PDEs). In this talk, we introduce the RBF method and discuss some of its basic properties. We follow this with an overview of some recent advances with the method, and some new research opportunities.