  This is my dissertation. Its research object is a symmetric group of
permutations acting on a finite set. The density of permutations with a given
cycle structure pattern is explored when the group order tends to infinity. New
and sharper asymptotic formulas are obtained. The latter are applied in
approximations of the cycle vector distribution of a random permutation. The
saddle-point method, Lagrange-B\"urmann inversion formula, Laplace
transformations, and other techniques of complex analysis are applied.
