Deep Reinforcement Learning (DRL) is attracting increasing interest due to its ability to learn how to solve complex tasks in an unknown environment solely by gathering experience. In this thesis, we investigate the use of DRL methods on the vision-based control of an autonomous quadcopter within a simulated environment. More specifically we employ an algorithm called Deep Q-network and two extensions involving the concept of Double Q-learning and Dueling Architecture. To evaluate the algorithms, we create a challenging task that concern obstacle avoidance and goal position reaching. Due to the lack of available tools that would combine the simulation of drones and the accessibility of DRL methods, we contribute AirGym as a framework that offers a convenient implementation of our task an these of following researchers. The results of the study support the idea of full control of an autonomous drone through DRL methods since we achieved an 80% success rate in solving the task under a near human-level of performance. This achievement is enhanced by considering the relatively short training time and the identification of further improvements.