The textbook outlines the foundations of modern mathematical statistics, limit theorems for empirical distributions and basic types of statistics, the foundations of the theory of estimates and the theory of hypothesis testing. Methods of finding optimal and asymptotically optimal procedures are considered. Considerable attention is paid to the statistics of differently distributed observations and, in particular, to the problems of homogeneity, problems of regression and discrete analysis, pattern recognition and the problem of discord. A single game-theoretic approach to the problems of mathematical statistics is presented. Statistical games and the basic principles of finding optimal and asymptotically optimal decisive rules are studied. Many results of valuation theory and hypothesis testing theory generalize to the case of an arbitrary loss function.