This dissertation investigates the application of Reinforcement Learning methods to the discovery of optimal routes in communication networks. Any current communication network displays dynamic behavior, changing its states over time. Therefore, the routing algorithms must react swiftly to changes in the network status. The objective of this work is to evaluate the application of some Reinforcement Learning techniques to define adaptive packet routing algorithms. The packet routing problem under the RL vision consists in the definition of each node on network as an RL agent. Thus, each agent must take actions in order to minimize an objective function such as end to end packet routing delay. One main objective of the RL is precisely learning to take the actions that minimize a given function. This thesis is consists of 4 main parts: first, a study of Reinforcement Learning (RL); a study of the communication networks and packet routing; the routing problem model as a RL system and the implementation of several RL methods in order to obtain some routing algorithms; e finally, the case study. The study of Reinforcement Learning extends from the more basic definitions, Reinforcement Learning features, elements of a RL system and environment modeling as a Markovian Decision Process, to the basic methods of solution: Dynamic Programming, Monte Carlo methods and Temporal Differences methods. In this last case, two specific algorithms have been considered: TD and Q-Learning, and, finally, the Eligibility Traces are evaluated as a useful tool that permits us to accelerate the learning process leading to the TD(lambda) and the Q(lambda) routing algorithms. The study on communication networks and packet routing involves the foundations of communication networks, packet switching, the packet routing problem, and adaptive and non- adaptive routing algorithms used at the present time. Communication networks are defined as a set of nodes connected through communication links. In order to send a message from a source node to a destination node usually the message is broken into segments called packets, and these are sent through other nodes until arriving at the destination. In this way the problem appears to choose the path which takes the shortest possible time for the packet to reach the destination node. The following algorithms have been analyzed: Shortest Path Routing that looks for paths with minimal hop number, not being sensible to the changes of load level and network topology; Weighted Shortest Path Routing that offers better performance from a global vision of the state of the network, which is not always easy to get in real networks; on the other hand, the Bellman- Ford routing algorithm was studied, this is based on local routing decisions and periodic updates, with some limitations to obtain policies in high load conditions. Bellman-Ford is one of the algorithms most used at the present time, being the basis for many existing routing protocols. The modeling of the routing problem as a RL system was inspired by one of the main features of the definition of an RL system: an agent who interacts with the environment and learns to reach an objective; therefore, the modeling of the routing algorithms has as its objective to learn to discover the paths that minimize packet routing time from an origin to an destination. The evaluation of a chosen route cannot be completed before the package reaches its final destination. This fact implies that supervised learning cannot be applied to the routing problem. On the other hand, Reinforcement Learning does not need a input-output pair for the learning process, allowing it to approach the problem with relative ease. In the modeling, each network node is viewed as a RL agent that acts in the same network; the network is the environment. The routing information is stored in the existing value functions in all nodes in the network, for each node and all another destination node