The book is devoted to the presentation of the statistical theory of pattern recognition. In the first part of the book, the problem of pattern recognition is considered from the point of view of the problem of minimizing average risk. It is shown how far you can go in solving the problem of training in pattern recognition, following each of the existing risk minimization paths in statistics, and what algorithms they lead to. The second part is devoted to the study of mathematic learning problems. The theory of uniform convergence of the frequencies of occurrences of events to their probabilities is presented, which is a limiting generalization of Glivenko's theorem. The third part is devoted to algorithms for constructing linear and piecewise linear solving rules. The book is designed for senior students, graduate students, engineers and researchers involved in the field of theoretical and technical cyber genetics. It will also be of interest to specialists in probability theory and mathematical statistics.