Neurons and Symbols, the successor to the authors' work An Introduction to Neural Computing, presents in a unified explanatory style the emerging points of a fierce contemporary debate on the effect that neural models are likely to have on more classic symbolic models of cognition. The controversy is multi-disciplinary - it involves scientists and technologists who are trying to build machines with cognitive properties, computer theoreticians interested in artificial intelligence, cognitive scientists and psychologists who are trying to find appropriate representations for cognition, philosophers who would like to explain concepts of the mind and linguists who are concerned with the role of language in cognition. The non-mathematical approach of this book lays bare the arguments that are put forward by those who, on the one hand, believe that the way to understand cognition is by knowing what the neural networks of the brain are doing, and on the other, those who believe that a program-like symbolic representation is the way to explain things. Is there a compromise between the two? The authors believe that there is and present the results of their own research in the area. Being interdisciplinary, one of the aims of the book is to start from first principles in everything, providing the reader with sufficient background in neural systems, artificial intelligence, cognitive science, automata theory and computational theory.