  On the basis of `$RTT=TTR$' formalism, we introduce the quantum double of the
Yangian $Y_{\hbar}(\gtg)$ for $\gtg=\gtgl_N,\gtsl_N$ with a central extension.
The Gauss decomposition of T-matrices gives us the so-called Drinfel'd
generators. Using these generators, we present some examples of both finite and
infinite dimensional representations that are quite natural deformations of the
corresponding affine counterpart.
