A collection of articles by leading foreign scientists (England, USA, Canada) devoted to one of the actively developing areas of modern mathematics, combining mathematics with physics The problem of the classification of monopoles and instantons, which arose in modern theoretical physics, led to new important results in mathematics, in particular algebraic geometry and topology. One of the most striking results of recent years - Donaldson's construction of exotic smooth structures on four-dimensional spheres - is found in the study of Yangmill stratifications. On the other hand, the use of new mathematical methods has made it possible to significantly advance the study of a number of important physical problems. For mathematicians of different specialties, theoretical physicists, graduate students and students .