Abstract: Electroencephalography (EEG) is a neuroimaging modality that captures the dynamics of brain activity well but suffers from high variability, low signal-to-noise ratio, and spatial resolution. It is extensively used in brain-computer interfaces (BCI), where the subject interacts with a computer through its brain signals. The challenge of BCI is to classify incoming data correctly. State-of-the-art methods are based on sample covariance matrices and their associated Riemannian geometry. Even though such approaches are effective, they have several limitations, such as the Gaussianity assumption or the need for very specific preprocessing. In this project, we propose exploiting geometry and robust statistics to develop original classification, clustering, and transfer learning methods suited to EEG data. We also plan to investigate the interest of registration methods for EEG in order to build reliable reference databases and improve transfer learning techniques. The practical interest of developed algorithms will be validated on real EEG data obtained from commonly used open BCI datasets.