The paper presents the result of comparative analysis of the main approaches to multi-class classification, synthesis of their mathematical models based on the considered algorithms is carried out. Their features, advantages, and disadvantages are presented, and the accuracy of multi-class classification is evaluated. Their features, advantages, and disadvantages are presented, and the accuracy of multi-class classification is evaluated. The dependence on accuracy and computational resource requirements is shown. The OvA algorithm can be a better way to solve problems with a small number of classes and limited resources. For tasks that require high classification accuracy and sufficient computational resources, AvA or OvO algorithms can be chosen. Synthesis of mathematical models and systematic generalization was carried out.