[1] The problems considered by Counting on Frameworks primarily concern systems of rigid rods, connected to each other by flexible joints at their ends; the question is whether these connections fix such a framework into a single position, or whether it can flex continuously through multiple positions.
[1][3][4] Counting on Frameworks expects its readers to be familiar with multivariable calculus, but beyond that level of background material it does not demand much mathematical sophistication.
[5] More generally, the editors of Mathematika recommend it to "Any reader with at least a slight mathematical background".
A more advanced and rigorous treatment of the same material can be found in Combinatorial Rigidity (1993), a graduate textbook co-authored by Graver.
[5] Reviewer Tiong Seng Tay describes it as "an excellent expository book".