Epilepsy is the fourth most common neurological disorder, affecting about 1% of the population at all ages. As many as 60% of people with epilepsy experience focal seizures which originate in a certain brain area and are limited to part of one cerebral hemisphere. In focal epilepsy patients, a precise surgical removal of the seizure onset zone can lead to effective seizure control or even a seizure-free outcome. Thus, correct identification of the seizure onset zone is essential. For clinical evaluation purposes, electroencephalography (EEG) recordings are commonly used. However, their interpretation is usually done manually by physicians and is time-consuming and error-prone. In this work, we propose an automated epileptic signal classification method based on modern deep learning methods. In contrast to previous approaches, the network is trained directly on the EEG recordings, avoiding hand-crafted feature extraction and selection procedures. This exploits the ability of deep neural networks to detect and extract relevant features automatically, that may be too complex or subtle to be noticed by humans. The proposed network structure is based on a convolutional neural network with residual connections. We demonstrate that our network produces state-of-the-art performance on two benchmark data sets, a data set from Bonn University and the Bern-Barcelona data set. We conclude that modern deep learning approaches can reach state-of-the-art performance on epileptic EEG classification and automated seizure onset zone identification tasks when trained on raw EEG data. This suggests that such approaches have potential for improving clinical practice.