There is an abundant literature on inequalities for the Gamma function Γ and its various related functions as well as their approximations. Only very recently, several authors began to investigate various inequalities for the double Gamma function Γ 2 and its approximation. Here, in this sequel to some of these recent works, we aim at presenting an integral representation of the triple Gamma function Γ 3 , which is then used to derive an asymptotic formula for Γ 3 . As a by-product of the results presented here, integral representations and asymptotic formulas for the Gamma function Γ and the double Gamma function Γ 2 are also given. The methods and techniques used in this paper can easily be extended to derive the corresponding integral representations and asymptotic formulas for the multiple Gamma functions Γ n (n≧4).