SageMath is by now a well-established system for computational mathematics. It is used by many researchers, as well as increasingly in classrooms. While there is a wealth of material online to learn it, including many published papers, there are few books squarely about SageMath itself--especially not advanced books.

Computational mathematics being SageMath’s forte, this book hews to that closely: Part 1 (five chapters) is an introduction to SageMath, meant to be widely accessible, followed by three more parts (each three or four chapters) covering algebra/analysis, numerical computations, and combinatorics, respectively. These latter parts are generally much more advanced.

The real strength of this book is the consistent approach that it takes: each part follows a tutorial style that mimics an interactive session, with well-chosen illustrative examples throughout; a few sections do fall prey to trying to be encyclopedic in their coverage of a topic by listing all the applicable commands, something which might have been more effectively done online. The use of color (for input, output, and graphs) adds to the book’s visual appeal. The online version is even more pleasant to peruse, as it is fully hyperlinked. Given how many authors the book has, this level of uniformity is impressive.

The authors are quite careful to point out the pitfalls of all computational mathematics systems--so much so that a true beginner might be put off (bugs are mentioned twice just in the preface). Of course, to graduate from novice to advanced user, these pitfalls are required knowledge, and it is nice to see the authors being quite honest about this.

The release of this book in English is quite timely. SageMath is gaining in popularity, and a solid reference for its more advanced use was overdue. The book could benefit readers who are interested in computational mathematics, prefer open-source systems, and are willing to live with a less polished system than the commercial alternatives.