This article is an excerpt from our Sefer
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In which months does one celebrate Purim? 
During a leap year Purim is celebrated in the second Adar. The reason for this is because we desire to proximate the Purim salvation to the redemption from Egypt, the redemption of Mordechai to the redemption of Moshe. We do not celebrate Purim twice as it is learned from a verse in Esther that we only celebrate Purim one time.
 Megillah 6b; Levush brought in Kaf Hachaim 697/1; The first month of Adar is the added month and not the second. [Gemara Rosh Hashanah 19b; See Yerushalmi Megillah 1/5]