This monograph presents the foundations of the probabilistic theory of stock exchanges, built on the basis of probabilistic economic theory. Analytical and numerical methods of this theory are used for calculation of temporal dynamics of market prices and trade volumes of various assets on the Moscow Exchange and Intercontinental Exchange Futures Europe during one trading session and a detailed comparison of the theoretical results with the corresponding experimental data. This comparison demonstrates a good agreement between the theory and experiment, which allows us to assert that the main scientif ic problem of this study is solved in the monograph, namely, it is shown that probabilistic economic theory finds its experimental confirmation and thereby acquires its solid experimental justification. This monograph may seem interesting to everyone who is engaged in research in economics, finance, econophysics or physical economics, as well as to professional investors and stock traders.