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This Special Issue of the journal Entropy, titled “Information Geometry I”, contains a collection of 17 papers concerning the foundations and applications of information geometry. Based on a geometrical interpretation of probability, information geometry has become a rich mathematical field employing the methods of differential geometry. It has numerous applications to data science, physics, and neuroscience. Presenting original research, yet written in an accessible, tutorial style, this collection of papers will be useful for scientists who are new to the field, while providing an excellent reference for the more experienced researcher. Several papers are written by authorities in the field, and topics cover the foundations of information geometry, as well as applications to statistics, Bayesian inference, machine learning, complex systems, physics, and neuroscience.

decomposable divergence --- tensor Sylvester matrix --- maximum pseudo-likelihood estimation --- matrix resultant --- ?) --- Markov random fields --- Fisher information --- Fisher information matrix --- Stein equation --- entropy --- Sylvester matrix --- information geometry --- stationary process --- (? --- dually flat structure --- information theory --- Bezout matrix --- Vandermonde matrix