'Crafted with evident care for the subject and the reader, Niu and Spivak invite us into the mathematically abundant world of polynomial functors. Their practical and pedagogical approach plants the seeds for a long, fruitful interaction between 'Poly' and those making sense of our dynamic and interconnected world.' Brendan Fong, Topos Institute

'This book by Niu and Spivak is a new perspective on automata and dynamical systems. It contains new kinds of mathematics, but is fun and easy to read. It is all about polynomials, but of a new kind. It is all about lenses, but what is a lens? Do you know that a Moore machine is a special kind of lens? That a polynomial comonoid is the same thing as a category? Do you know what a retrofunctor is? The book answers all these questions and more. It offers plenty of solved exercises.' André Joyal, Université du Québec à Montréal

'In this lovingly illustrated volume, Niu and Spivak gift the reader an admirably accessible treasure trove offering profound value for addressing challenges in diverse application areas, including databases, dynamical systems, simulation, programming language semantics and type theory. It is hard to overstate the contribution of this book, so full of wonderfully explicated concepts, insightful examples, and thought-provoking exercises that build readers' capacity to actualize the potential of polynomial functors in their own spheres of interest.' Nathaniel Osgood, Computational Epidemiology & Public Health Informatics Laboratory, University of Saskatchewan