  In this work, we construct fundamental domains for congruence subgroups of
$SL_2(F_q[t])$ and $PGL_2(F_q[t])$. Our method uses Gekeler's description of
the fundamental domains on the Bruhat- Tits tree $X = X_{q+1}$ in terms of
cosets of subgroups. We compute the fundamental domains for a number of
congruence subgroups explicitly as graphs of groups using the computer algebra
system Magma.
