The question "What would have happened if." is still seen by many historians as a useless dalliance. Alexander Demandt, however, recalls Friedrich Schiller's claim that culture unfolds only through playing games. If this is true, then it is also true for science. The playful occupation with possibilities is as important to science as controled and scheduled work according to tried and true methods. The core of this short volume consists not only of imagining and thinking up historical alternatives - what would have happened if Hitler had died in 1938? What would have happened if the Peasants' War of 1525 had succeeded? What if Pontius Pilate had set Jesus free? If Hannibal had marched on Rome after his victory at Cannae? In original and sometimes "brilliant diction" (Frank Schirrmacher, review in FAZ) Demandt points out that and how the thinking up of unrealized alternatives can be justified as part of the study of history.