The transport coefficients of the Anderson model require knowledge of both the temperature and frequency dependence of the single--particle spectral densities and consequently have proven difficult quantities to calculate. Here we show how these quantities can be calculated via an extension of Wilsons numerical renormalization group method. Accurate results are obtained in all parameter regimes and for the full range of temperatures of interest ranging from the high temperature perturbative regime $T>>T_{K}$, through the cross--over region $Tapprox T_{K}$, and into the low temperature strong coupling regime $T<<T_{K}$. The Fermi liquid relations for the $T^2$ coefficient of the resistivity and the linear coefficient of the thermopower are satisfied to a high degree of accuracy. The techniques used here provide a new highly accurate approach to strongly correlated electrons in high dimensions.
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