The collection is devoted to the introduction to the intensively developing direction of modern number theory related to the construction of non-commutative class field theory. Methods of algebraic number theory, L-functions, group representations and algebraic geometry play an equal role in the formulation of the main problem and its partial solution. Among the authors of the articles are famous mathematicians: T. Springer (Holland), A. Borel, Dk. Tait (USA), P. Deligne (France).