This revised edition of Ryuzo Sato's seminal work illustrates the timeless nature of his contribution to economics. It is as pertinent today as when it was originally conceived, over twenty years ago. The book deals with a variety of topics in economic theory, ranging from the analysis of production functions to the general recoverability problem of optimal dynamic behavior. They are unified in the theme of 'transformation and invariance'. This book demonstrates the first application of the Lie Theory to modern economics and provides a revealing analysis of market behavior and economic invariance. The book will be of interest to scholars of industrial economics, innovation, econometrics and microeconomics.