The book was written on the basis of lectures that were given by the author for many years in the 3rd year of the Faculty of Mathematics of Novosibirsk University. The book covers a wide range of issues, including 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 for finding optimal and asymptotically optimal procedures are described in particular. The book is designed for graduate students and students of mathematical and physical specialties of higher educational institutions.