Information Geometry of the Probability Simplex: A Short Course

This set of notes is intended for a short course aiming to provide an (almost) self-contained and (almost) elementary introduction to the topic of Information Geometry (IG) of the probability simplex. Such a course can be considered an introduction to the original monograph by Amari and Nagaoka (2000), and to the recent monographs by Amari (2016} and by Ay et al. (2017). The focus is on a non-parametric approach, that is, I consider the geometry of the full probability simplex and compare the IG formalism with what is classically done in Statistical Physics.