Subdivision methods in computer graphics constitute a large class of recursive schemes for computing curves and surfaces. They seem to have their origin in the geometric problem of smoothing the corners of a given polyhedral surface - in fact, these methods are sometimes called "wood carver" algorithms because the repeated smoothing operations are ogous to sculpting wood. This book presents a systematic development of the basic mathematical principles and concepts associated with stationary subdivision algorithms. The authors pay special attention to the structure of such algorithms in a multidimensional setting and yse the convergence issue using appropriate tools from Fourier ysis and functional ysis. The ytic structure of the limiting curves and surfaces is revealed in two ways: the smoothness of these surfaces is determined by certain algebraic properties of the algorithm, while the highest order derivatives of the limiting surfaces are shown to be fractals. Scientists interested in computer graphics, splines, wavelets, and multiresolution ysis will find the ytic and algebraic tools developed here more than useful.