  The Maker-Breaker domination game is played on a graph $G$ by Dominator and
Staller. The players alternatively select a vertex of $G$ that was not yet
chosen in the course of the game. Dominator wins if at some point the vertices
he has chosen form a dominating set. Staller wins if Dominator cannot form a
dominating set. In this paper we introduce the Maker-Breaker domination number
$\gamma_{{\rm MB}}(G)$ of $G$ as the minimum number of moves of Dominator to
win the game provided that he has a winning strategy and is the first to play.
If Staller plays first, then the corresponding invariant is denoted
$\gamma_{{\rm MB}}'(G)$. Comparing the two invariants it turns out that they
behave much differently than the related game domination numbers. The invariant
$\gamma_{{\rm MB}}(G)$ is also compared with the domination number. Using the
Erd\H{o}s-Selfridge Criterion a large class of graphs $G$ is found for which
$\gamma_{{\rm MB}}(G) > \gamma(G)$ holds. Residual graphs are introduced and
used to bound/determine $\gamma_{{\rm MB}}(G)$ and $\gamma_{{\rm MB}}'(G)$.
Using residual graphs, $\gamma_{{\rm MB}}(T)$ and $\gamma_{{\rm MB}}'(T)$ are
determined for an arbitrary tree. The invariants are also obtained for cycles
and bounded for union of graphs. A list of open problems and directions for
further investigations is given.
