  We define the Laplacian matrix and the Jacobian group of a finite graph of
groups. We prove analogues of the matrix tree theorem and the class number
formula for the order of the Jacobian of a graph of groups. Given a group $G$
acting on a graph $X$, we define natural pushforward and pullback maps between
the Jacobian groups of $X$ and the quotient graph of groups $X/\!/G$. For the
case $G=\mathbb{Z}/2\mathbb{Z}$, we also prove a combinatorial formula for the
order of the kernel of the pushforward map.
