Methods of Information Geometry (Amari, S. and Nagaoka, H.; 2000) [Book review]

This book presents the state of the art, the current best practices and the innovative techniques of the methods of information geometry. The first half of the book presents a comprehensive introduction to the mathematical foundation of information geometry, including preliminaries from differential geometry, the geometry of manifolds or probability distributions, and the general theory of dual affine connections. The second half describes many applications, such as statistics, linear systems, information theory, quantum mechanics, convex analysis, neural networks, and affine differential geometry. This is a well-written book, original and highly relevant from which to learn methods and results.