This volume gives a systematic account of various problems of statistical diagnostics - the detection of changes in probabilistic characteristics of random processes and fields. Methods of solving such problems are proposed, based upon a unified non-parametric approach. Two general formalizations of the problems of statistical diagnostics are considered: firstly, the detection of changes in arbitrary probabilistic distributions of random processes and fields, "glued" from different stationary pieces - in other words, the detection of moments or areas of such "glueing"; and secondly, the detection of statistical "contamination" in data (realizations of random fields or processes), or "abnormal" observations with deviating statistical characteristics. A general approach to solving such problems is proposed, which is based upon the principle of reduction to certain standard situations and which does not use a priori data about probabilistic distributions. Much attention is paid to applications in such diverse areas as biology (EECs) and economics. The book should be of interest to researchers in statistics and random processes, as well as advanced undergraduate and postgraduate students in the same disciplines, and to specialists in control theory, systems analysis, biomedical engineering, and econometrics.