This is a book for all mathematicians and for mathematically trained scientists in other fields. It is not just for those interested in entropy or diversity for their own sakes, but anyone who enjoys discovering unexpected connections within mathematics and beyond. The global biodiversity crisis is one of humanity's most urgent problems. However, even quantifying biological diversity is a difficult conceptual challenge. This book brings new mathematical rigour to the ongoing debate. It applies the power of the axiomatic method to a biological problem of pressing concern, but it also presents new theorems that stand up as mathematics in their own right, independently of any application. The question "what is diversity?" has surprising mathematical depth. This book also calls on a wide range of mathematics, touching on subjects including: functional equations information theory geometric measure theory category theory probability theory number theory. Even so, the mathematical prerequisites are few: the main narrative thread requires no more than an undergraduate course in analysis. Publication The book was published by Cambridge University Press in April 2021 and is now in all good bookshops. You can order it directly from CUP in paperback or hardback. A free version is also available as arXiv:2012.02113. The cover shows the Great Blue Hole. Legal text for the arXiv version: This material has been published by Cambridge University Press as Entropy and Diversity: The Axiomatic Approach by Tom Leinster. This version is free to view and download for personal use only. Not for re-distribution, re-sale or use in derivative works. © Tom Leinster 2020. Errata Here is a list of corrections. If you find any others, however small, please let me know: Firstname.Lastname@ed.ac.uk.   This page was last changed on 31 October 2022. Home