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The monograph considers the fundamentals of systems theory and mathematical modeling using the principles of the systems approach. In the monograph, much attention is paid to set-theoretic, dynamic, as well as aggregative and combined models. Based on the group-theoretical approach, a generalization of the theory of signals, their characteristics are considered, their classification and some theorems are carried out. A separate chapter is devoted to mathematical models of signal interaction with the propagation medium. The monograph also considers mathematical models of stochastic signal processing and control systems based on spline filtering, artificial intelligence models and neural networks. The monograph can be useful for a wide range of specialists in various fields of knowledge dealing with mathematical modeling in their research, and can also be used as a teaching aid for conducting both classroom and independent theoretical and practical classes with bachelors, masters, graduate students in the discipline "System Theory and System Analysis", "Mathematical Modeling" and "Optimal and Suboptimal Estimation of Random Processes and Systems".