Geoopt is a research-oriented modular open-source package for Riemannian Optimization in PyTorch. The core of Geoopt is a standard Manifold interface that allows for the generic implementation of optimization algorithms. Geoopt supports basic Riemannian SGD as well as adaptive optimization algorithms. Geoopt also provides several algorithms and arithmetic methods for supported manifolds, which allow composing geometry-aware neural network layers that can be integrated with existing models.