Gemara

18b - Rav and R. Chanina: Megilas Ta'anis is Batel (does not apply nowadays);

R. Yochanan and R. Yehoshua ben Levi: It is not Batel.

Question (against Rav - Beraisa): A case occurred, and a fast was decreed in Lud on Chanukah. R. Eliezer bathed, R. Yehoshua cut his hair, and they told the people that they transgressed by fasting.

Answer (Rav Yosef): Chanukah is different, since the miracle is well known (it is improper to Mevatel it).

Ta'anis 15b - Mishnah: For any day in Megilas Ta'anis on which we may not (even) eulogize, the day before is forbidden, but the following day is permitted;

R. Yosi forbids both of them.

17b - Beraisa: The days before and after the days in Megilas Ta'anis are forbidden. Shabbos and Yom Tov are forbidden, but before and after them is permitted.

Question: What is the difference between them?

Answer: We need to be more stringent to strengthen the days in Megilas Ta'anis because they are mid'Rabanan.

18a - Rav Ashi: Even though Megilas Ta'anis lists Adar 28, Megilas Ta'anis also needed to list Rosh Chodesh Nisan (to forbid eulogies on the 29th). The day after (a day in Megilas Ta'anis) it is forbidden to fast but permitted to eulogize.

Beraisa - R. Shimon ben Gamliel: It says 'on them' twice in Megilas Ta'anis, to teach that the days themselves are forbidden, but before and after them are permitted.

Rav and R. Yochanan: The Halachah follows R. Yosi.

Shmuel: The Halachah follows R. Shimon ben Gamliel.

R. Chiya bar Aba: R. Yochanan rules like R. Yosi (only) regarding fasting.

18b: Rav Nachman decreed a fast on the 12th (of Adar).

Rabanan: This is Yom Torainus (it is in Megilas Ta'anis)!

Rav Nachman: Yom Torainus was Batel, because Shemayah and Achiyah were killed that day.

Question: Still, it is forbidden for it is the day before Yom Nikanor!

Answer Rav Ashi: Yom Torainus itself was Batel because of the tragedy that occurred on it. All the more so the Isur to fast due to the following day is Batel!

Rosh Hashanah 19b: The Halachah is, Megilas Ta'anis is not Batel regarding Chanukah and Purim. It is Batel regarding everything else.

Rishonim

Rif and Rosh (Ta'anis 2:24): The days before and after the days in Megilas Ta'anis are forbidden. Shabbos and Yom Tov are forbidden, but before and after them is permitted. Because they are mid'Oraisa, we need not strengthen them. Nowadays Megilas Ta'anis is Batel, except for Chanukah and Purim.

Rif (Megilah 4a): The Halachah follows R. Yosi, who forbids before and after. Even though R. Chiya bar Aba said that R. Yochanan rules like R. Yosi only regarding fasting, we hold like Rav Ashi, who says that the following day it is forbidden to eulogize but permitted to fast.

Ran (DH umid'Amrinan): These words are not from the Rif. They are an addition from R. Efrayim.

Rebuttal (Ba'al ha'Ma'or): The Rif's text is mistaken. We are more lenient about eulogies than fasting! Also, Rav Ashi did not come to teach the Halachah, rather, to explain why Megilas Ta'anis lists Rosh Chodesh Nisan. Nowadays, only Chanukah and Purim are forbidden. The days after are totally permitted, and only fasting is forbidden the day before them. For people in open cities, the 14th of Adar is forbidden by Divrei Kabalah, so we may fast Ta'anis Esther the day before. For people in walled cities the 14th is forbidden only because of Megilas Ta'anis, therefore it needs to be strengthened, so they may not fast on the 13th.

Milchamos Hash-m: Because Chachamim sought to be lenient, we rule like Shmuel who permits the days before and after, against Rav and R. Yochanan.

Rambam (Hilchos Megilah 2:13): No one in any place may fast or eulogize on the 14th and 15th of Adar Rishon or Sheni, whether he lives in a walled or open city.

Rambam (Hilchos Chanukah 3:3): Because of the miracles of the war and the oil, Chachamim enacted that the eight days beginning with Kislev 25 are days of Simchah... Fasting and eulogies are forbidden, like on Purim.

Rambam (Hilchos Evel 11:3): We do not eulogize on Chanukah or Purim, but we may eulogize before or after them.

Kesef Mishneh: Before and after Chanukah and Purim are no better than the other Yomim Tovim of Megilas Ta'anis, which are Batel.

Ra'avad (brought in Rosh, ibid. and Ran DH Aval): Megilas Ta'anis is Batel regarding individuals, but we may not decree a fast on those days. We learn from Rav Nachman. He defended his decree to fast on Yom Torainus by saying 'Yom Torainus was Batel.' It did not suffice to say that Megilas Ta'anis is Batel!

Rebuttal (Ran, ibid.): The Gemara (Rosh Hashanah 18b) asked why a fast was decreed on Chanukah, since Megilas Ta'anis still applies to it. We infer that we may decree a fast on days such as Yom Nikanor which were Batel. Rav Nachman's Talmidim asked him in order to learn whether or not he holds that Megilas Ta'anis was Batel. He answered that even if it was not Batel, fasting would be permitted.

Poskim

Shulchan Aruch (573:1): Megilas Ta'anis is Batel. One may fast on those days, and all the more so the days before and after them. The exceptions are Chanukah and Purim. Those days are forbidden, but before and after them are permitted.

Beis Yosef (DH u'Mah she'Chosav Rabeinu): The Tur cites the Ra'avad, who says that it is not Batel to permit decreeing a fast on days in Megilas Ta'anis. The Ran refuted this, and the custom is unlike the Ra'avad.

Tur (586): Before and after Chanukah and Purim are no better than the other Yomim Tovim of Megilas Ta'anis, which are Batel.

Rema: One who gets married on Chanukah should not fast.

Mishnah Berurah (6): All the more so one who gets married on Purim should not fast, for they are days of Simchah and feasting.

Shulchan Aruch (670:1): Fasting and eulogies are forbidden during the eight days of Chanukah.

Shulchan Aruch (3): (On Chanukah) we eulogize only a Chacham in front of him.

Rema: We do not fast on the Yartzite of a parent (on Chanukah).

Shulchan Aruch (686:1): One may fast before and after Chanukah and Purim.

Hagahos Maimoniyos (Hilchos Evel 11:3): R. Shavat says that before and after Chanukah and Purim is permitted, because everyone knows about the miracle. It is the custom is of Yisrael to fast the day before Purim. His 'proof' from Ta'anis Esther does not prove that optional fasts are permitted.

Mishnah Berurah (1): The Bach forbids to fast the day before Chanukah. Some places (which normally fast every Yom Kipur Katan, i.e. Erev Rosh Chodesh) fast then to compensate for Erev Rosh Chodesh Teves, on which it is forbidden to fast. One should not change the custom, but it is better not to conduct that way. Surely we do not decree a Ta'anis Tzibur. The same applies to the day after Chanukah.

Kaf ha'Chayim (5): Since Yom Kipur Katan is not on the proper day anyway, it is better to fast two days before Chanukah to fulfill all opinions.

Kaf ha'Chayim (3): The Bach permits to fast the day after Chanukah, and the Shulchan Aruch and many permit even the day before, so one may be lenient about the day after.