Utility theory or, value theory in general, is certainly the cornerstone of decision theory, game theory, microecon~mics, and all social and political theories which deal with public decisions. Recently the American School of utility, founded by von N eumann­ Morgenstern, encountered a far-going criticism by the French School of utility represented by its founder Allais. The whole basis of the theory of decisions involving risk has been shaken and put into question. Consequently, basic research in the fundamentals of utility and value theory evolved into a crisis. Like any crisis in basic research, and this one was not an exception, it was very fruitful. One may simply say: Allais versus von Neumann-Morgenstern, or the French School of utility versus the American School, became one of the battlefields of scientific development which proved to be a most creative source of new advances and new developments in all those sciences which are based on evaluation of utilities.

Introductory Survey.- The Foundations of a Positive Theory of Choice involving Risk and a Criticism of the Postulates and Axioms of the American School.- CriticaI Examination of the New Foundation of Utility.- A Short Confirmation of My Standpoint.- Utilities, Psychological Values, and Decision Makers.- Some Reflections on Utility.- A Reply to Allais.- Utility and Stochastic Dominance.- Maximizing Expected Utility and the Rule of Long Run Success.- Adaptive Utility.- On the Nature of Expected Utility.- The St. Petersburg Puzzle.- Towards a Positive Theory of Preferences Under Risk.- The Naturalistic Versus the Intuitionistic School of Values.- Utility Theory: Axioms versus `Paradoxes¿.- Comparison of Decision Models and some Suggestions.- The So-called Allais Paradox and Rational Decisions Under Uncertainty.- Subject Indexes.- - Parts I (Foreword), II and V.- - Allais¿ notation.- - Parts I (Introductory Survey), III and IV.- Name Index.