In this seminar, I address the construction of parallel transport in the setting of non-collapsed RCD(K,N) spaces, i.e. infinitesimally Hilbertian mms verifying a synthetic notion of lower bound on the Ricci curvature and upper bound on the dimension, equipped with the N-dimensional Hausdorff measure. In this generality, we cannot study parallel transport along a single curve, but along a well distributed family of flow lines, in a sense related to the notion of regular Lagrangian flows in the non smooth setting. After a brief introduction to the theory of RLF in the non smooth setting, I address how, in a joint work with N. Gigli and E. Pasqualetto, we obtained existence and uniqueness of parallel transport in this setting. To be more specific, we established a Leibniz formula granting uniqueness and I would like to emphasize the functional analytic tools developed for the proof of this formula.