Appears in collection : Séminaire Poincaré XXIII - L'information

What is Shannon’s information theory (IT)? Despite its continuedimpact on our digital society, Claude Shannon’s life and work is still unknown to numerous people. In this tutorial, we review many aspects of the concept of entropy and information from a historical and mathematical point of view. The text is structured into small, mostly independent sections, each coveringa particular topic. For simplicity we restrict our attention to one-dimensional variables and use logarithm and exponential notations log and exp without specifying the base. We culminate with a simple exposition of a recent proof (2017) of the entropy power inequality (EPI), one of the most fascinating inequality in the theory.