The PhD subject deals with geometric deep learning and its use in several medical applications. The merging of these two domains (geometry and artificial intelligence) is at the core of the phD with the conception of SPDnet neural networks that combine both end-to-end training of frequency and spatial parameters with mathematical operations on the variety of symmetric definite-positive (SPD) matrices. The design of such methods both from a mathematical and software point of view are part of the phD’s objectives as well as their application on public medical datasets like in electroencephalography-based brain-computer interface (BCI). The expected results consist first in demonstrating the superiority of these geometric approaches over state-of-the-art methods used in BCI and second to identify the best architectures in different medical applications ranging from multi-array data to medical image processing.