Artificial Intelligence (AI) became today perhaps the most up-to-date topic in many areas. One of the main goals of AI is to create completely autonomous agents able to interact with the surrounding world and learn by trial and error optimal behaviors in different contexts, perfectible in time. Among the machine learning methods of AI, reinforcement learning (RL) by repetitive interactions with the environment while targeting a purpose plays a particularly important role, besides supervised and unsupervised learning. However, classical RL methods have important limitations in scalability to higher-dimensionality problems. In recent years, supervised and unsupervised learning technologies based on deep learning, using deep neural networks with remarkable properties of approximating complex functions on multi-dimensional spaces, as well as the learning of characteristic hierarchical representations automatically extracted directly from data, with significant dimensional reduction, have had an explosive development, producing astonishing results comparable with, or even surpasing human performance in areas such as object / image recognition, speech recognition, automatic translation etc. The combination of RL with deep learning methods has led to what is now called deep reinforcement learning (DRL), providing new possibilities for producing autonomous agents in multidimensional spaces. This paper is proposing a brief presentation of the DRL field, while also studying and analyzing in detail one of the first successful DRL methods, namely Deep Q-Network developed by Google DeepMind.