High-energy gamma radiation is created in the most extreme conditions in the universe, such as in those near a supermassive black hole or a neutron star. When very-high-energy gamma rays interact with the atmosphere, they create a shower of secondary particles. Some of these particles are charged and superluminal and in the interaction with the atmosphere, such secondary particles produce Cherenkov light that can be detected by imaging atmospheric Cherenkov telescopes like MAGIC. Unfortunately for gamma astronomy, the universe is full of high-energy cosmic rays that interact with the atmosphere in a very similar way to gamma rays. As the detected signal-to-noise ratio is extremely low, the standard analysis uses machine learning methods trained on parameterized images of recorded events. Like any parameterization, it implies an irreversible loss of information. An approach that uses deep learning methods, specifically convolutional neural networks, could improve the accuracy of the analysis by avoiding parameterization and instead learning from the raw image pixels themselves. This thesis proposes a chain of analysis for the reconstruction of events recorded by MAGIC telescopes using convolutional neural networks. The reconstruction tasks are reduced to a binary classification task (signal and noise separation) and two regression tasks (reconstruction of the energy and direction of the primary particle). LeNet and AlexNet architectures were trained and tested on cleaned and uncleaned data, as well as on single-channel (charge information) and two-channel (charge and time information) data, which gives a total of 8 trained models per task, or 24 trained models in total. The performances of all the models are presented in the last chapter.