The book is intended for an initial acquaintance with the mathematical foundations of modern machine learning theory (Machine Learning) and prediction game theory. The first part outlines the foundations of the statistical theory of machine learning, considers the problems of classification and regression with reference vectors, the theory of generalization and algorithms for constructing dividing hyperplanes. The second and third parts consider adaptive prediction problems in non-stochastic game theoretic and comparative productions: predictions using expert strategies and prediction games. For undergraduate and graduate students specializing in machine learning and artificial intelligence.