Our study is based on the hypothesis that stock exchanges, being nonlinear, open and dissipative systems, are capable of self-organization to the edge of a phase transition. To empirically support the hypothesis, we find segments in hourly stock volume series for 3,000 stocks of publicly traded companies, corresponding to the time of stock exchange's stay to the edge of a phase transition. We provide a theoretical justification of the hypothesis and present a phenomenological model of stock exchange self-organization to the edge of the first-order phase transition and to the edge of the second-order phase transition. In the model, the controlling parameter is entropy as a measure of uncertainty of information about a share of a public company, guided by which stock exchange players make a decision to buy/sell it. The order parameter is determined by the number of buy/sell transactions by stock exchange players of a public company's shares, i.e., stock's volume. By applying statistical tests and the AUC metric, we found the most effective early warning measures from the set of investigated critical deceleration measures, multifractal measures and reconstructed phase space measures. The practical significance of our study is determined by the possibility of early warning of self-organization of stock exchanges to the edge of a phase transition and can be extended with high frequency data in the future research.