Gemara

R. Yehoshua ben Levi: Mikra Megilah is obligatory upon women because they were also in the miracle.

19b - Mishnah: All may read the Megilah, except for a Cheresh, lunatic or child;

R. Yehuda permits a child.

Erchin 2b - Question: A Beraisa teaches 'Mikra Megilah is obligatory upon everyone'. A Mishnah teaches that 'Everyone is Kosher to read the Megilah' - whom is included?

Answer: Women are included, like R. Yehoshua ben Levi taught:

R. Yehoshua ben Levi: Women are obligated to read the Megilah, because the miracle also saved (or involved) women.

Rishonim

Rif: Mikra Megilah is obligatory upon women because they were also in the miracle.

Ran (DH Nashim): This means that they were in danger and were saved, like it says in the Yerushalmi and like it says regarding the four cups on Pesach (Pesachim 108b).

Ran (6b DH Masnisin): Some say that according to the opinion that requires a Minyan for Mikra Megilah, women do not join, just like they do not join for a Zimun. This is unreasonable. Since they can Motzi men regarding Megilah, surely they join! Regarding Zimun they do not join due to Pritzus (indecency). This does not apply to Kri'as ha'Megilah, for there is no change in the way it is read when there is a Minyan, so it is not evident that they join.

Rambam (Hilchos Megilah 1:1,2): Everyone is obligated to read the Megilah; men, women... One who reads or hears is Yotzei, as long as he hears from one who is obligated. Therefore, one who hears from a child or lunatic is not Yotzei.

Magid Mishnah: The Rambam seems to hold that a woman can be Motzi the Rabim.

Rosh (1:4): Mikra Megilah is obligatory upon women because they were also in the miracle. These words connote that women can read it and Motzi men. Also in Erchin the Gemara says that the Mishnah includes women to read the Megilah, i.e. and they can Motzi men. In Erchin, Rashi explains like this.

BaHaG (brought in Rosh ibid.): Women are obligated only to hear the Megilah because they were in danger and were saved, but they cannot read to be Motzi men. A man must hear from a man obligated like himself for it to be considered as if he read.

Source (Tosefta 2:4): Kri'as ha'Megilah is obligatory upon everyone, i.e. Kohanim, Leviyim...Mamzerim, Serisim...all of these are obligated and can be Motzi the Rabim. An Androginus can be Motzi another Androginus, but not anyone else. A Tumtum or a half slave cannot be Motzi anyone. Women, slaves and children are exempt; they cannot be Motzi the Rabim.

Rosh (ibid.): BaHaG must explain the Gemara in Erchin to teach that a woman can read for another woman. A woman need not hear a more distinguished reading from a man.

Hagahos Maimoniyos (1): According to BaHaG we do not say that women can be Motzi men because both are obligated mid'Rabanan. This is because women are not obligated to read, only to hear.

Poskim

Shulchan Aruch (689:1): Everyone is obligated to read the Megilah; men, women, and freed slaves.

Beis Yosef (DH u'Mah she'Chosav v'Avadim): We need not mention slaves. They are like women, i.e. they are obligated to hear, but not to read. Since slaves are circumcised, they were also in danger and saved by the miracle. However, according to those who explain that women are obligated because they were involved in the miracle, slaves are exempt, for it is a Mitzvas Aseh sheha'Zeman Gerama.

Kaf ha'Chayim (3): Some question how a woman is Yotzei by listening in the Ezras Nashim, for she cannot hear properly there. Indeed, if she did not hear properly she must hear again, e.g. in the house.

Shulchan Aruch (ibid. 2): One who reads or hears is Yotzei, as long as he hears from one who is obligated. Therefore, one who hears from a Cheresh, child or lunatic is not Yotzei. Some say that women are not Motzi men.

Beis Yosef (DH u'Mah she'Chosav Rabeinu b'Shem): In BaHaG's text in Erchin, R. Yehoshua ben Levi says that women are obligated to hear the Megilah. This is why the Tosefta is not difficult for him. BaHaG must explain that the Mishnah (Everyone is Kosher to read the Megilah) includes a woman, i.e. she can be Motzi other women.

Gra (DH v'Yesh Omrim): The first opinion holds that the Gemara rejects the Tosefta, for it contradicts itself (the Reisha says 'everyone' to include women, and the Seifa excludes women. Presumably, they discuss the same matter, i.e. to be Motzi men.)

Kaf ha'Chayim (13): Kri'as ha'Megilah is unlike Ner Chanukah (in which women can be Motzi men), because it is like Kri'as ha'Torah. I.e., it is not honorable for a woman to be Motzi the Tzibur. We do not distinguish, and she cannot Motzi even an individual. Also, some say that a woman is not obligated to read, only to hear, therefore she cannot Motzi men. Some say that she cannot Motzi men because a woman's voice is Ervah. The first opinion permits because this is not considered singing.

Rema: Some say that if a woman reads for herself she blesses 'to hear the Megilah' for she is not obligated to read it.

Mishnah Berurah (8): A woman should hear from men. If this is not possible, she reads for herself. However, she should not Motzi many women, for this is belittling (Sha'ar ha'Tziyon 15).

Kaf ha'Chayim (19): Some say that if women hear from a man who was already Yotzei, no Berachah is made.