This is a book about Gröbner bases and their applications. It contains 3 chapters, 20 sections, 44 tutorials, 165 exercises, and numerous further amusements. It is going to help you bridge the gap between theoretical computer algebra and actual computation. We hope you will have as much fun reading it as the authors had writing it! From the reviews: "This is one of the most refreshing mathematical books I have ever held in my hands. This is academic teaching at its best; if I had not seen it, I would not have believed that it could be done so well." (Hans Stetter, IMN - Internationale Mathematische Nachrichten 2003) "Every paragraph of the book shows how much the authors have enjoyed translating into printed matter the outcome of a long, large, deep and personal relation with computationally oriented commutative algebra. And the result is a non-standard, elementary and self-contained introduction to the theory of Gröbner bases and its applications." (Laureano González-Vega and Tomás Recio, ACM SIGSAM Bulletin 2004) "The style of this book merits a comment. Each section begins with a quotation and an overview in which "Italian imagination overtakes German rigor". These introductions and the following main bodies of each section are well written, engaging and often amusing. The book is a pleasure to read." (John Little, Mathematical Reviews 2001).