This program is mainly a study of invariants of not only the entire class of growth functions of a finitely generated group but also particular growth functions within that class. The goals are to extend the class of groups whose growth functions are known to be always rational, and to study further the growth functions that can occur for geometric groups. The attempt to show that rationality of the growth functions is independent of the generating set will be in the spirit of Cannon's work. The study of the growth functions that occur will continue the work of Floyd and Plotnick on planar groups. Special attention will be paid to reciprocity of the growth functions and to when the value at 1 is the reciprocal of the Euler characteristic. Many surprising and easily stated facts about geometric groups have been uncovered empirically, and it is time to bring some order into the area.
