This work describes a new mathematical concept of modeling field theory and its applications to a variety of problems while offering a view of the relationships among mathematics, computational concepts in neural networks, semiotics, and concepts of mind in psychology and philosophy. The book is directed towards a diverse audience of students, teachers, researchers, and engineers working in the areas of neural networkss, artificial intelligence, cognitive science, fuzzy systems, pattern recognition and machine/computer vision, data mining, robotics, target tracking, sensor fusion, spectrum analysis, time series analysis, and financial market forecasting. Mathematically inclined philosophers, semioticians, and psychologists will also find many areas of interest. Modeling field neural networks utilize internal "world" models. The concept of internal models of the mind originated in artifical intelligence and cognitive psychology, but its roots date back to Plato and Aristotle. Intelligent systems based on rules utlize models in their final conceptual forms of rules. Like the Eide (Ideas) of Plato, rules lack adaptivity. In modeling field theory, the adaptive models are similar to the Forms of Aristotle and serve as the basis for learning. By combining the a priori knowledge with learning, the most perplexing problems in field of neural networks and intelligent systems are addresses: fast learning and robust generalization. The new mathematics describes a basic instinct for learning and the related affective signals in the learning process. An ability to perceive beauty is shown to be an essential property of adaptive system related to the instinct for learning. The combination of intuition with mathematics provides the foundation of a physical theory of mind. The book reviews most of the mathematical concepts and engineering approaches to the development of intelligent systems discussed since the 1940s. The origin of the Aristotelian mathematics of mind is traced in Grossberg's ART neural network; and its essential component turns to be fuzzy logic. Among the topics disucssed are hierarchical and heterarchical organization of intelligent systems, statistical learning theory, genetic algorithms, complex adaptive systems, mathematical semiotics, the dynamical nature of symbols, Godel theorems and intelligence, emotions and thinking, mathematics of emotional intellect, and consciousness. The author's striking conclusion is that philosphers of the past have been closer to the computational concepts emerging today than pattern recognition and AI experts of just a few years ago.