The book offers a new theoretical framework for modern statistical inference problems, generally referred to as learning problems. They arise in connection with hard operational problems to be solved in the lack of all necessary knowledge. The success of their solutions lies in a suitable mix of computational skill in processing the available data and sophisticated attitude in stating logical relations between their properties and the expected behavior of candidate solutions. The framework is discussed through rigorous mathematical statements in the province of probability theory. But this does not prevent the authors from grounding the presentation in the immediate intuition of the reader, writing a highly comprehensive style and coloring it with examples from everyday life. The first two chapters describe the theoretical framework, dealing respectively with probability models and basilar inference tools. The third chapter presents the computational learning theory. The fourth chapter deals with problems of linear and nonlinear regression, while the fifth chapter throws a statistical perspective on the universe of neural networks examining various approaches, including hybridations with classical AI systems.