The paper under review computes the Cartan matrix for the finite group $G={\rm Sp}(6,3)=\bold{G}(\bold{F}_3)$, the rational points of the quasisimple algebraic $k$-group $\bold{G}={\rm Sp}(6,k)$ over the field of 3 elements; here $k$ is an algebraic closure of $\bold{F}_3$. \par More generally, for any simple algebraic $k$-group $\bold{G}$ defined over the prime field $\bold{F}_p$, the entries in the Cartan matrix of interest are the multiplicities $[U_L\colon L']$, where $L$ and $L'$ are simple $kG$-modules (with $G=\bold{G}(\bold{F}_p)$), and where $U_L$ is the $G$-projective cover of $L$. In this setting, $L$ and $L'$ have the structure of $\bold{G}$-modules, and they restrict irreducibly to $\bold{G}_1 \cdot \bold{T}$, where we have denoted by $\bold{G}_1$ and $\bold{T}$, respectively, the first Frobenius kernel of and a maximal torus of $\bold{G}$. \par As the authors note, the injective hull $Q_L$ of $L$ as a $\bold{G}_1 \cdot \bold{T}$-module is known to have the structure of a $\bold{G}$-module when its high weight satisfies certain conditions; this fact was proved by Humphreys, Jantzen, and---for the higher Frobenius kernels---Koppinen. When $Q_L$ indeed has a $\bold{G}$-module structure, its restriction to $G$ is projective and contains $U_L$ with multiplicity 1. It is not known whether or not $Q_L$ has a $\bold{G}$-module structure in general. However, even if it does not, its formal character ${\rm ch}(Q_L)$ lifts to $\bold{G}$ and it makes sense as a Brauer character, in fact, as a Brauer character of a projective $k[G]$-module; see for example §2.5 of [J. C. Jantzen, in {\it The Arcata Conference on Representations of Finite Groups (Arcata, Calif., 1986)}, 127--146, Proc. Sympos. Pure Math., 47, Part 1, Amer. Math. Soc., Providence, RI, 1987; MR0933356 (89g:20076)]. So far as this reviewer can determine, the authors do not mention the possibility that $Q_L$ has no $\bold{G}$-module structure, though they seem to use that fact implictly. \par Returning to $\bold{G}={\rm Sp}(6,k)$, the authors use a formula due to Chastkofsky and Jantzen to compute all multiplicities $(*) \ [{\rm ch}(Q_L)\colon{\rm ch}(U_{L'})]$, and hence to compute the Cartan matrix. Though it is not mentioned in the paper, it is true quite generally that the matrix of the multiplicities $(*)$ is unipotent upper triangular; hence knowledge of $(*)$ is enough to compute the Cartan matrix provided one knows enough about the relationship between Weyl characters for $\bold{G}$ and the characters of the simple $\bold{G}$-modules. For this group, the authors have the required knowledge thanks to the paper by J. C. Ye\ and Z. Zhou\ [Comm. Algebra {\bf 29} (2001), no.~1, 201--223; MR1842492 (2002e:20087)]. Apparently they also use a computer and the software package MATLAB, though details regarding these computations are not given in the paper.