  We associate a group $IMG(f)$ to every covering $f$ of a topological space
$M$ by its open subset. It is the quotient of the fundamental group $\pi_1(M)$
by the intersection of the kernels of its monodromy action for the iterates
$f^n$. Every iterated monodromy group comes together with a naturally defined
action on a rooted tree. We present an effective method to compute this action
and show how the dynamics of $f$ is related to the group. In particular, the
Julia set of $f$ can be reconstructed from $\img(f)$ (from its action on the
tree), if $f$ is expanding.
