  A book $B_n$ is a graph which consists of $n$ triangles sharing a common
edge. In this paper, we study Ramsey numbers of quadrilateral versus books.
Previous results give the exact value of $r(C_4,B_n)$ for $1\le n\le 14$. We
aim to show the exact value of $r(C_4,B_n)$ for infinitely many $n$. To achieve
this, we first prove that $r(C_4,B_{(m-1)^2+(t-2)})\le m^2+t$ for $m\ge4$ and
$0 \leq t \leq m-1$. This improves upon a result by Faudree, Rousseau and
Sheehan (1978) which states that \begin{align*} r(C_4,B_n)\le g(g(n)),
\;\;\text{where}\;\;g(n)=n+\lfloor\sqrt{n-1}\rfloor+2. \end{align*} Combining
the new upper bound and constructions of $C_4$-free graphs, we are able to
determine the exact value of $r(C_4,B_n)$ for infinitely many $n$. As a special
case, we show $r(C_4,B_{q^2-q-2}) = q^2+q-1$ for all prime power $q\ge4$.
