In this thesis, we explore reinforcement learning in the game of guarding a territory which is played in the continuous domain. We make the assumption that the players have no a priori knowledge of their optimal behaviors. Therefore, we apply reinforcement learning to train the players to find their optimal behaviors. To our knowledge, this is the first investigation of both the invader and the guard learning simultaneously. In addition, we look at the possibility of an invader which is superior (faster) to a group of guards. To determine the optimal solution of the game when the players have different speeds and evaluate the players’ learning performance, we apply the Apollonius circle approach. This is the first application of the Apollonius circle approach to the guarding a territory game that we know of. Simulation results from this study show that the players are able to learn their optimal strategies simultaneously.