The book outlines the theory of inverse problems often found in physics and engineering. Based on the concepts of mathematical statistics, a number of well-known methods of information circulation are analyzed, in particular: the optimal filtration of Kolmogorov-Wiener, the method of maximum entropy, the regularization of Phillips-Tikhonov and image recovery using iterative procedures. It is shown that the consistent application of statistical methods, taking into account the a priori information actually available to the researcher, allows to obtain stable and effective solutions to inverse problems. Theoretical consideration is accompanied by a large number of examples; summaries of calculation formulas. are given. As applications, the problem of the limiting resolution of optical devices, the classical problem of non-parametric evaluation of the power spectrum of the time series and the phase problem that has been relevant in recent years are studied. The book is designed for specialists in various fields of science and technology. It is available to students of universities and technical educational institutions. Related books: 1. Tikhonov A . N. , Arsenin V. I. Methods of solving incorrect problems . - Science, 1979 2. Sizikov V. C. Sustainable methods of processing measurement results. - Spets . Lith, 1999 Book submitted to the site by KL. Alexy