The basis of a small book by a famous English mathematician is the recent work of E. Witten binding open B. Jones polynomial node invariants with topological quantum field theory. The focus is on clarifying ideas and motivations. The Russian translation is supplemented by an extended recording of the author's lectures on the geometry of the Yang-Mills fields, where the problem of finding all the instantons for the Yang-Mills equations is solved. The technique developed by mathematicians in this field is little known to physicists. One of the goals of the author is to try to bridge this gap between mathematicians and physicists, explaining the relevant technique as simply as possible and illustrating its application to finding instantons. For mathematicians-theoreticians and appliedists, as well as theoretical physicists.