In 1982, Springer published the English translation of the Russian book, "Estimation of Dependencies Based on Empirical Data" which became the foundation of the statistical theory of learning and generalization (the VC theory). A number of new principles and new technologies of learning, including SVM technology, have been developed based on this theory. The second edition of this book contains two parts: a reprint of the first edition which provides the classical foundation of Statistical Learning Theory; four new chapters describing the latest ideas in the development of statistical inference methods. They form the second part of the book entitled "Empirical Inference Science". The second part of the book discusses along with new models of inference the general philosophical principles of making inferences from observations. It includes new paradigms of inference that use non-inductive methods appropriate for a complex world, in contrast to inductive methods of inference developed in the classical philosophy of science for a simple world. The two parts of the book cover a wide spectrum of ideas related to the essence of intelligence: from the rigorous statistical foundation of learning models to broad philosophical imperatives for generalization. The book is intended for researchers who deal with a variety of problems in empirical inference: statisticians, mathematicians, physicists, computer scientists, and philosophers.