Riemann is an R package for learning with data on Riemannian manifolds. In statistics and machine learning, the term manifold appears in two realms; one is dimensionality reduction where we assume that low-dimensional data manifold is embedded in high-dimensional Euclidean space. The other is statistics on manifolds - data lie on some Riemannian manifolds that we are already well aware of. Riemann aims at the latter. If you are interested in dimension reduction, please check another R package Rdimtools.