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Epilepsy is the second most common brain disorder after migraine. Automatic detection of epileptic seizures can considerably improve the patients' quality of life. Current Electroencephalogram (EEG)-based seizure detection systems encounter many challenges in real-life situations. The EEGs are non-stationary signals and seizure patterns vary across patients and recording sessions. Moreover, EEG data are prone to numerous noise types that negatively affect the detection accuracy of epileptic seizures. To address these challenges, we introduce the use of a deep learning-based approach that automatically learns the discriminative EEG features of epileptic seizures. Specifically, to reveal the correlation between successive data samples, the time-series EEG data are first segmented into a sequence of non-overlapping epochs. Second, Long Short-Term Memory (LSTM) network is used to learn the high-level representations of the normal and the seizure EEG patterns. Third, these representations are fed into Softmax function for training and classification. The results on a well-known benchmark clinical dataset demonstrate the superiority of the proposed approach over the existing state-of-the-art methods. Furthermore, our approach is shown to be robust in noisy and real-life conditions. Compared to current methods that are quite sensitive to noise, the proposed method maintains its high detection performance in the presence of common EEG artifacts (muscle activities and eye-blinking) as well as white noise.