The theory of extreme value statistics is applied to the first, second, and third largest geomagnetic storms in nine solar cycles measured by the average half-daily aa indices compiled by Mayaud. Analytic expressions giving the probability of the extremes per solar cycle as a contnuour function of storm magnitude are obtained by least squares fitting of the observations to the appropriate theoretical extreme value probability functions. The results are used to obtain the statistical characteristics (mode, median, mean, and standard deviation) for the extreme values. The results are applied to find the expected range of extreme values in a set as a function of the number of solar cycles in the set. We find that the expected range of the larget storm is quite narrow and is larger for the second and third larget storms. The observed range of the extreme half-daily aa index for the nine solar cycles is 354--546 &ggr;. In a set of 100 cycles the range is expanded esentially to 311--680&ggr;, an increase of only 39% in the range. The result supports the argument for a change in solar cycle statistics in the latter part of the Seventeenth Century (the Maunder minimum).