By providing a clear exposition of the mathematical ideas that unify this field, Mathematical Foundations of Learning Machines offers the basis of a rigorous and integrated theory of Neural Networks. This seminal book is a recognized classic among Neural Network researchers due to Nilsson's presentation of intuitive geometric and statistical theories. Recent developments in Neural Networks and Artificial Intelligence underscore the importance of the strong theoretical basis for research in these areas. Many of the issues raised in this book still stand as challenges to current efforts, giving new relevance to the importance of proper formulation, analysis, experimentation, and then reformulation. Included in this volume are discussions of special relevance to learning rates, nonparametric training methods, nonlinear network models, and related issues from computation, control theory and statistics. The emphasis on deterministic methods for solving classification problems is an excellent starting point for readers interested in the probabilistic studies associated with Neural Networks research. Anyone interested in the foundations of Neural Networks and learning in parallel distributed processing systems will find this a valuable book.