This volume of twelve interlocked essays in mathematical economics deals with a central problem of modern economic theory: the search for a path to an optimum level of economic growth. The meaning of the Golden Rule concept is thoroughly expounded, and certain analogues are presented to show that the fundamental notion of a commanding growth path is encountered even in models in which no pure and simple Golden Rule path exists. The Golden Rule concept is tested and applied to a number of theoretical formulations and then extended to several kinds of investment other than capital formation, as the author postulates a Golden Rule of Research, a Golden Rule of Education, and even a concept dealing with population control-a Golden Rule of Procreation. This thorough and original work is important reading for students of macroeconomic theory, growth, development, and capital theory.