Historical Comments Two-dimensional random walks in domains with non-smooth boundaries inter- est several groups of the mathematical community. In fact these objects are encountered in pure probabilistic problems, as well as in applications involv- ing queueing theory. This monograph aims at promoting original mathematical methods to determine the invariant measure of such processes. Moreover, as it will emerge later, these methods can also be employed to characterize the transient behavior. It is worth to place our work in its historical context. This book has three sources. l. Boundary...