This thesis investigates the use of reinforcement learning to learn to drive a racecar in the simulated environment of the Robot Automobile Racing Simulator. Real-life race driving is known to be difficult for humans, and expert human drivers use complex sequences of actions. There are a large number of variables, some of which change stochastically and all of which may affect the outcome. This makes driving a promising domain for testing and developing Machine Learning techniques that have the potential to be robust enough to work in the real world. Therefore the principles of the algorithms from this work may be applicable to a range of problems. The investigation starts by finding a suitable data structure to represent the information learnt. This is tested using supervised learning. Reinforcement learning is added and roughly tuned, and the supervised learning is then removed. A simple tabular representation is found satisfactory, and this avoids difficulties with more complex methods and allows the investigation to concentrate on the essentials of learning. Various reward sources are tested and a combination of three are found to produce the best performance. Exploration of the problem space is investigated. Results show exploration is essential but controlling how much is done is also important. It turns out the learning episodes need to be very long and because of this the task needs to be treated as continuous by using discounting to limit the size of the variables stored. Eligibility traces are used with success to make the learning more efficient. The tabular representation is made more compact by hashing and more accurate by using smaller buckets. This slows the learning but produces better driving. The improvement given by a rough form of generalisation indicates the replacement of the tabular method by a function approximator is warranted. These results show reinforcement learning can work within the Robot Automobile Racing Simulator, and lay the foundations for building a more efficient and competitive agent.