The orbit counting problem has been studied in various contexts, from the circle problem studied by Gauss to lattice point counting in hyperbolic spaces in the 20^th century. In this talk we try to see the applications of some Tauberian theorems in dynamics for obtaining an asymptotic formula of number of words of finite length of specific property in symbolic space. The transfer operator and especially the spectral theory of the transfer operator establishes the bridge from themodynamics formalism to the Tauberian theorems for this purpose.