This paper presents the novel Riemannian Fusion Network (RFNet), a deep neural architecture for learning spatial and temporal information from Electroencephalogram (EEG) for a number of different EEG-based Brain Computer Interface (BCI) tasks and applications. The spatial information relies on Spatial Covariance Matrices (SCM) of multi-channel EEG, whose space form a Riemannian Manifold due to the Symmetric and Positive Definite structure... We exploit a Riemannian approach to map spatial information onto feature vectors in Euclidean space. The temporal information characterized by features based on differential entropy and logarithm power spectrum density is extracted from different windows through time. Our network then learns the temporal information by employing a deep long short-term memory network with a soft attention mechanism. The output of the attention mechanism is used as the temporal feature vector. To effectively fuse 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 from three popular fields of BCI, notably emotion recognition, vigilance estimation, and motor imagery classification, containing various types of tasks such as binary classification, multi-class classification, and regression. RFNet approaches the state-of-the-art on one dataset (SEED) and outperforms other methods on the other three datasets (SEED-VIG, BCI-IV 2A, and BCI-IV 2B), setting new state-of-the-art values and showing the robustness of our framework in EEG representation learning. (read more)