  We introduce geomstats, a python package that performs computations on
manifolds such as hyperspheres, hyperbolic spaces, spaces of symmetric positive
definite matrices and Lie groups of transformations. We provide efficient and
extensively unit-tested implementations of these manifolds, together with
useful Riemannian metrics and associated Exponential and Logarithm maps. The
corresponding geodesic distances provide a range of intuitive choices of
Machine Learning loss functions. We also give the corresponding Riemannian
gradients. The operations implemented in geomstats are available with different
computing backends such as numpy, tensorflow and keras. We have enabled GPU
implementation and integrated geomstats manifold computations into keras deep
learning framework. This paper also presents a review of manifolds in machine
learning and an overview of the geomstats package with examples demonstrating
its use for efficient and user-friendly Riemannian geometry.
