The crystallization of double alloys in systems with continuous solid and liquid solutions, with eutectic and peritectic transformations, as well as in a complex double system with a temperature minimum, intermediate phases and with specified crystallization transformations. is considered. Examples of ongoing processes with detailed quantitative calculations are given, in which knowledge of analytical geometry and differential analysis. is required. The equilibrium crystallization of alloys, determined by the state diagrams of double systems, as well as non-equilibrium crystallization according to the Petrov-Sheil model . Intended for the training course "Fundamentals of the theory of foundry processes", provided by the curriculum for bachelors in the direction of "Metallurgy" . ;Griff:Admitted by the educational and methodological association for education in the field of metallurgy as a teaching aid for students of higher educational institutions studying in the direction of 150400 Metallurgy