An algorithm utilizing a syntactic approach and a criterion based on normalized moments is developed for the reliable, automatic, machine recognition of handwritten and printed Greek characters of any size and font. In this approach a binary image of the character in question is obtained initially; its skeleton is then produced by utilizing a standard thinning algorithm. The classification process then incorporates the topological features of the characters such as existence of closed curves, number of intersections, number and location of free ends, axial symmetry, and the criteria derived from normalized moments to uniquely identify each pattern. An alternate approach involving a mathematical (geometrical) modeling of each character is also proposed. In this method, each character is to be individually modeled to a standard geometrical shape and the least-mean-square method is used to form the best fit. Characters like alpha, beta, gamma, omega, theta, omicron, and rho have been modeled with standard geometrical shapes such as circles, lemniscates, cardioids, ellipses and lines. Experiments conducted for both approaches demonstrated a very high recognition rate.