Unlike related books, this handbook brings together background material, derivations, and applications of differential entropy. The book first reviews probability theory as it enables an understanding of the core building block of entropy. The authors then carefully explain both discrete and differential entropy. They present detailed derivations of differential entropy for numerous probability models, discuss challenges with interpreting and deriving differential entropy, and show how differential entropy varies as a function of the model variance. They also explore the application of differential entropy in several areas.