Mishnah Megillah 2:1

If one reads the Megillah out of order, he has not fulfilled his obligation. If he reads it by heart, if he reads it in a translation [targum], or in any other language, he has not fulfilled his obligation. But they may read it to those who do not understand Hebrew in a language other than Hebrew. One who doesn’t understand Hebrew who heard it in Assyrian [Hebrew], has fulfilled his obligation.

הַקּוֹרֵא אֶת הַמְּגִלָּה לְמַפְרֵעַ, לֹא יָצָא. קְרָאָהּ עַל פֶּה, קְרָאָהּ תַּרְגּוּם, בְּכָל לָשׁוֹן, לֹא יָצָא. אֲבָל קוֹרִין אוֹתָהּ לַלּוֹעֲזוֹת בְּלַעַז. וְהַלּוֹעֵז שֶׁשָּׁמַע אַשּׁוּרִית, יָצָא:

Babylonian Talmud, Folio 17a–19a (on Mishnah 2:1–2)
Jerusalem Talmud, Halakhah 2:1

Mishnah Megillah 2:2

If one reads it with breaks, or naps [in between readings], he has fulfilled his obligation. If he was copying it, explaining it or correcting [a scroll of Esther], if he directed his heart, he has fulfilled his obligation, but if not, he has not fulfilled his obligation. If it was written with arsenic, with red chalk, with gum or with sulfate of copper, or on paper or on scratch paper, he has not fulfilled his obligation, unless it is written in Assyrian on parchment and in ink.

קְרָאָהּ סֵרוּגִין, וּמִתְנַמְנֵם, יָצָא. הָיָה כוֹתְבָהּ, דּוֹרְשָׁהּ, וּמַגִּיהָהּ, אִם כִּוֵּן לִבּוֹ, יָצָא. וְאִם לָאו, לֹא יָצָא. הָיְתָה כְּתוּבָה בְּסַם, וּבְסִקְרָא, וּבְקוֹמוֹס וּבְקַנְקַנְתּוֹם, עַל הַנְּיָר וְעַל הַדִּפְתְּרָא, לֹא יָצָא, עַד שֶׁתְּהֵא כְּתוּבָה אַשּׁוּרִית, עַל הַסֵּפֶר וּבִדְיוֹ:

The Babylonian Talmud discusses this mishnah with 2:1 above.

Jerusalem Talmud, Halakhah 2:2

Mishnah Megillah 2:3

A resident of a town who has gone to a walled city or a resident of a walled city who has gone to a town, if he is to return to his own place he reads according to the rule of his own place, and if not reads with them. From where does a man read the Megillah and thereby fulfill his obligation? Rabbi Meir says: all of it. Rabbi Judah says: from “There was a Jew” (Esther 2:5). Rabbi Yose says: from “After these things” (Esther 3:1).

בֶּן עִיר שֶׁהָלַךְ לִכְרַךְ וּבֶן כְּרַךְ שֶׁהָלַךְ לְעִיר, אִם עָתִיד לַחֲזֹר לִמְקוֹמוֹ, קוֹרֵא כִמְקוֹמוֹ. וְאִם לָאו, קוֹרֵא עִמָּהֶן. וּמֵהֵיכָן קוֹרֵא אָדָם אֶת הַמְּגִלָּה וְיוֹצֵא בָּהּ יְדֵי חוֹבָתוֹ, רַבִּי מֵאִיר אוֹמֵר, כֻּלָּהּ. רַבִּי יְהוּדָה אוֹמֵר, מֵאִישׁ יְהוּדִי (אסתר ב ה). רַבִּי יוֹסֵי אוֹמֵר, מֵאַחַר הַדְּבָרִים הָאֵלֶּה (אסתר ג׳:א׳):

Babylonian Talmud, Folio 19a–19b
Jerusalem Talmud, Halakhah 2:3
Jerusalem Talmud, Halakhah 2:4

Mishnah Megillah 2:4

All are qualified to read the Megillah except a deaf person, an idiot and a minor. Rabbi Judah qualifies a minor. They do not read the Megillah, nor circumcise, nor go to the mikveh, nor sprinkling [purificatory waters], and similarly a woman keeping day for day should not take a ritual bath until the sun has risen. But if any of these things is done after dawn, it is valid.

הַכֹּל כְּשֵׁרִין לִקְרוֹת אֶת הַמְּגִלָּה, חוּץ מֵחֵרֵשׁ, שׁוֹטֶה, וְקָטָן. רַבִּי יְהוּדָה מַכְשִׁיר בְּקָטָן. אֵין קוֹרִין אֶת הַמְּגִלָּה, וְלֹא מָלִין, וְלֹא טוֹבְלִין, וְלֹא מַזִּין, וְכֵן שׁוֹמֶרֶת יוֹם כְּנֶגֶד יוֹם לֹא תִטְבֹּל, עַד שֶׁתָּנֵץ הַחַמָּה. וְכֻלָּן שֶׁעָשׂוּ מִשֶּׁעָלָה עַמּוּד הַשַּׁחַר, כָּשֵׁר:

Babylonian Talmud, Folio 19b–20a
Babylonian Talmud, Folio 20a–20b
Jerusalem Talmud, Halakhah 2:5

Mishnah Megillah 2:5

The whole day is a valid time for reading the Megillah; reciting Hallel; for the blowing of the shofar; for taking up the lulav; for the Musaf prayer; for Musaf sacrifices; for confession over the oxen; for the confession over the tithe; for the confession of sins on Yom HaKippurim; for laying on of hands; for slaughtering [the sacrifices]; for waving [them]; for bringing near [the vessel with the minhah-offering to the altar]; for taking a handful; for placing it on the fire; for pinching off [the head of a bird-offering]; for receiving the blood [in a vessel]; for sprinkling [the blood on the altar]; for making the sotah drink [the bitter waters]; for breaking the neck of the heifer; and for purifying the metzora.

כָּל הַיּוֹם כָּשֵׁר לִקְרִיאַת הַמְּגִלָּה, וְלִקְרִיאַת הַהַלֵּל, וְלִתְקִיעַת שׁוֹפָר, וְלִנְטִילַת לוּלָב, וְלִתְפִלַּת הַמּוּסָפִין, וְלַמּוּסָפִין, וּלְוִדּוּי הַפָּרִים, וּלְוִדּוּי הַמַּעֲשֵׂר, וּלְוִדּוּי יוֹם הַכִּפּוּרִים, לַסְּמִיכָה, לַשְּׁחִיטָה, לַתְּנוּפָה, לַהַגָּשָׁה, לַקְּמִיצָה וְלַהַקְטָרָה, לַמְּלִיקָה, וְלַקַּבָּלָה, וְלַהַזָּיָה, וּלְהַשְׁקָיַת סוֹטָה, וְלַעֲרִיפַת הָעֶגְלָה, וּלְטַהֲרַת הַמְּצֹרָע:

Babylonian Talmud, Folio 20b–21a (on Mishnah 2:5–6)
Jerusalem Talmud, Halakhah 2:6

Mishnah Megillah 2:6

The whole night is valid for reaping the Omer and for burning fat and limbs [on the altar]. This is the general principle: any matter whose commandment is during the day, is valid all day and any matter whose commandment is at night is valid all night.

כָּל הַלַּיְלָה כָּשֵׁר לִקְצִירַת הָעֹמֶר וּלְהֶקְטֵר חֲלָבִים וְאֵבָרִים. זֶה הַכְּלָל, דָּבָר שֶׁמִּצְוָתוֹ בַיּוֹם, כָּשֵׁר כָּל הַיּוֹם. דָּבָר שֶׁמִּצְוָתוֹ בַלַּיְלָה, כָּשֵׁר כָּל הַלָּיְלָה:

The Babylonian Talmud discusses this mishnah with 2:5 above.

Jerusalem Talmud, Halakhah 2:7

The Mishnah: English translation: Joshua Kulp, Mishnah Yomit (Conservative Yeshiva), via Sefaria, licensed CC BY; changes made (line breaks, spacing, a typo, and Kulp's study notes removed from five mishnayot). Hebrew: Torat Emet 357, public domain; Bikkurim chapter 4 from Dan Be'eri's edition of the Kaufmann manuscript, public domain.

The Jerusalem Talmud: English translation and Hebrew/Aramaic text: Heinrich W. Guggenheimer, The Jerusalem Talmud: Edition, Translation, and Commentary (Berlin: De Gruyter, 1999-2015), via Sefaria, licensed CC BY 4.0; changes made (his footnotes and the page markers removed).

The Babylonian Talmud: English: Berakhot, A. Cohen, The Babylonian Talmud: Tractate Berakot (Cambridge University Press, 1921), public domain; Sukkah and Megillah, Daf Shevui (Conservative Yeshiva), CC0; Ta'anit, Henry Malter, The Treatise Ta'anit of the Babylonian Talmud (Jewish Publication Society, 1928), public domain; Chagigah, A. W. Streane, A Translation of the Treatise Chagigah from the Babylonian Talmud (Cambridge University Press, 1891), public domain; Makkot, Sefaria Community Translation, CC0. Hebrew and Aramaic: Ta'anit, Malter's critical text (1928, public domain; his notes not reproduced); the others, Wikisource Talmud Bavli (Vilna edition), via Sefaria, licensed CC BY-SA 3.0 (this site's cleaned copy of that text is shared under the same license); changes made (markup and images removed).