This is the book I wish I had read when I was a graduate student...The book fulfills its role as an invitation to the realm of nonlinear algebra, not only for students but also for working mathematicians in other areas, although more advanced arguments naturally require further reading. By browsing this book one can taste the flavour of a growing and developing topic. The strategic choice of the 13 chapters is important in itself. The text is interactive and invites the readers to google some key words to get further information and to experience for themselves several paradigmatic examples with a computer algebra system. Also, several interesting applications are sketched or exemplified.

The text is likely to be an inspiration for the up-and-coming graduate student as well as an established mathematician who is looking to widen the scope of their work. By drawing on topics from a wide range of pure and applied mathematics and weaving them into a single narrative, the authors convince us that nonlinear algebra is a discipline to which we should all be introduced.

... this book provides a highly accessible and very well-written introduction to the vast and exciting field of nonlinear algebra. The chapters are designed so as to be able to serve as a guideline for a graduate course in this field. Nevertheless, one can easily use this book for self-study and it is even usable for advanced undergraduates in mathematics. Given its high quality of writing and abundant examples that illustrate deep concepts in an easy-to-understand manner, I would expect that this book will serve as the classical textbook of this topic for many years to come.