That is, it concerns equations between two integer-valued formulas, shown to be equal either by showing that both sides of the equation count the same type of mathematical objects, or by finding a one-to-one correspondence between the different types of object that they count.
The book provides combinatorial proofs of thirteen theorems in combinatorics and 246 numbered identities (collated in an appendix).
[4][6] Additionally, many of the book's chapters are themselves self-contained, allowing for arbitrary reading orders or for excerpts of this material to be used in classes.
[2] Echoing this, reviewer Joe Roberts writes that despite its elementary nature, this book should be "valuable as a reference ... for anyone working with such identities".
[5] Reviewer Gerald L. Alexanderson describes the book's proofs as "ingenious, concrete and memorable".
"[8] One of the open problems from the book, seeking a bijective proof of an identity combining binomial coefficients with Fibonacci numbers, was subsequently answered positively by Doron Zeilberger.
In the web site where he links a preprint of his paper, Zeilberger writes, "When I was young and handsome, I couldn't see an identity without trying to prove it bijectively.
But the urge got rekindled, when I read Arthur Benjamin and Jennifer Quinn's masterpiece Proofs that Really Count.