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We present a novel deep neural architecture for learning electroencephalogram (EEG). To learn the spatial information, our model first obtains the Riemannian mean and distance from spatial covariance matrices (SCMs) on a Riemannian manifold. We then project the spatial information onto a Euclidean space via tangent space learning. Following, two fully connected layers are used to learn the spatial information embeddings. Moreover, our proposed method learns the temporal information via differential entropy and logarithm power spectrum density features extracted from EEG signals in a Euclidean space using a deep long short-term memory network with a soft attention mechanism. To combine the spatial and temporal information, we use an effective fusion strategy, which learns attention weights applied to embedding-specific features for decision making. We evaluate our proposed framework on four public datasets across three popular EEG-related tasks, notably emotion recognition, vigilance estimation, and motor imagery classification, containing various types of tasks such as binary classification, multi-class classification, and regression. Our proposed architecture outperforms other methods on SEED-VIG, and approaches the state-of-the-art on the other three datasets (SEED, BCI-IV 2A, and BCI-IV 2B), showing the robustness of our framework in EEG representation learning. The source code of our paper is publicly available at https://github.com/guangyizhangbci/EEG_Riemannian.