Extending the Stone Duality Theorem, we prove two duality theorems for the category ZHaus of zero-dimensional Hausdorff spaces and continuous maps. They extend also the Tarski Duality Theorem; the latter is even derived from one of them. We prove as well two new duality theorems for the category EDTych of extremally disconnected Tychonoff spaces and continuous maps. Also, we describe two categories which are dually equivalent to the category ZComp of zero-dimensional Hausdorff compactifications of zero-dimensional Hausdorff spaces and obtain as a corollary the Dwinger Theorem about zero-dimensional compactifications of a zero-dimensional Hausdorff space.