Numerous connections exist between Torah study and the Purim miracle.
It states (Esther 8:16) אורה היתה ליהודים, 'The Yidden had light...' Chazal say that this means they had Torah. Rashi explains that Haman made a decree against studying the Torah, and now that the miracles and the salvation began, they were permitted once again to study Torah. Yesod v'Shoresh HoAvodah (Hamifkad 6) writes, "We understand from this the great obligation for all people who know how to learn Torah to learn it and be happy with the Torah on Purim. You should praise Hashem with your mouth and thoughts that Hashem foiled Haman's plan, who wanted to forbid us from studying Torah."
The Gemara (Shabbos 88.) also tells us that when the miracle occurred, due to the nation's love to Hashem for the miracle, the Yidden accepted the Torah again. Years before, the Torah was given on Har Sinai, but then the nation was forced to accept the Torah. If they didn't accept the Torah, Hashem told them they would be buried under the mountain. But at the time of the Purim miracle, they accepted the Torah again, this time out of love rather than fear. This source also indicates to us the connection between Purim and the study of Torah, and it is another indication that one should devote time to study Torah on Purim.
Chazal say that the final day of Achashveirosh's party was on a Shabbos. The goyim were speaking nivul peh and the Yidden were speaking divrei Torah and singing zemiros to Hashem. Ben Yehoyada says that in this merit the salvation began. Vashti was killed at the party, making a place for Esther to save the Jewish nation. It was the vast difference between Yidden and the goyim, that was seen at this party, that saved us. The study of Torah saved the Jewish nation, and it is appropriate to study Torah on Purim.
In particular, the Rema writes we should study some Torah before the Purim seudah as a segulah and shemirah that nothing inappropriate occurs at the seudah.
The Chasam Sofer's Tradition
The Chasam Sofer zt'l (Drushim v'Agados p.245) writes, "I received from Reb Mendele Lilig zt'l who was the Rav in Frankfurt, who received it from the gaon Shev Yaakov zt'l, that whoever studies Torah between the megillah at night and the megillah in the morning, he is guaranteed to be a ben Olam HaBa. This is how I received it; I don’t know the reason."
The Chasam Sofer (Drashos vol.1, Purim 5596) says that Purim should have been on the thirteenth of Adar because that is when the Yidden won the war against their enemies. Why do we celebrate on the following day, the day after the war ended? It is to ensure that there will always be a place in the world where Torah will be studied. If the celebration would be on the thirteenth, the day they fought the war, everyone would have Purim on the same day. And due to the many celebrations, the world would be without Torah. Therefore, Chazal established Purim on the day they rested from the war. Thus, Purim is celebrated on two days. Unwalled cities celebrate Purim on the fourteenth of Adar, and walled cities celebrate Purim on the fifteenth. In this way, there will always be people studying Torah. Because when it is Purim in the walled cities, those without walls aren't celebrating Purim, and vice versa. Thereby, there will always be some people studying Torah in the world.
The Pele Yoetz (in Yaalzu Chasidim) writes, "I heard about a certain Rav who studied most of the night of Purim. He said that on this night, people eat and drink and are happy, and Hakadosh Baruch Hu doesn't have anyone studying Torah. Therefore, I will study Torah, and my Torah will be precious to Hashem."
