Geometric and topological inference deals with the retrieval of information about a geometric object that is only known through a finite set of possibly noisy sample points. Geometric and topological inference employs many tools from Computational Geometry and Applied Topology. It has connections to Manifold Learning and provides the mathematical and algorithmic foundations of the rapidly evolving field of Topological Data Analysis. Building on a rigorous treatment of simplicial complexes and distance functions, this book covers various aspects of the field, from data representation and combinatorial questions to manifold reconstruction and persistent homology. This first book on the subject can serve for teaching in a mathematical or computer science department, and will benefit to scientists and engineers interested in a geometric approach to Data Science.