This book constitutes the refereed proceedings of the Third International Conference on Geometric Science of Information, GSI 2017, held in Paris, France, in November 2017. The 101 full papers presented were carefully reviewed and selected from 113 submissions and are organized into the following subjects:  Statistics on non-linear data Shape Space Optimal Transport & Applications I (Data Science and Economics) Optimal Transport & Applications II (Signal and Image Processing) Topology and statistical learning Statistical Manifold & Hessian Information Geometry Monotone Embedding in Information Geometry Information Structure in Neuroscience Geometric Robotics & Tracking Geometric Mechanics & Robotics Stochastic Geometric Mechanics & Lie Group Thermodynamics Probability on Riemannian Manifolds Divergence Geometry Geometric Deep Learning First and second-order Optimization on Statistical Manifolds Non-parametric Information Geometry Geometry of quantum states Optimization on Manifold Computational Information Geometry Probability Density Estimation Geometry of Tensor-Valued Data Geometry and Inverse Problems Geometry in Vision, Learning and Dynamical Systems Lie Groups and Wavelets Geometry of metric measure spaces Geometry and Telecom Geodesic Methods with Constraints Applications of Distance Geometry.