This thesis applies Reinforcement Learning (RL) and Fuzzy Logic to the problem of creating a robust routing algorithm for potential application in a Quality of Service environment with multiple classes of traffic.A value based RL scheme was developed that was a similar to one previously developed by Littman and Boyan [7], but whereas the latter utilized packet hop counts as a reward measure, the RL scheme employed throughout this document uses delay as the primary reward metric. Alternatively, any aggregated QOS measure can be substituted in place of delay, to suit the needs of the particular application environment. This modified scheme was applied in a 10 node network environment that generated packet traffic based on statistics collected from UTORLINK, which monitors packet activity on the back bone of the University of Toronto's networks. This thesis examined the theoretical 'best' and 'worst' topological cases for any N node network, and used these formulas to calculate long term expected hop counts.