Gemara

(Beraisa - R. Meir): It does not say 'the Mitzvos that Yisre'elim will do and live in them', rather, "that a man will do and live in them"! This teaches that a Nochri who engages in Torah is (rewarded) like a Kohen Gadol.

He is rewarded less than one who is not commanded and fulfills.

Kidushin 29b: "V'Limadtem" may be read 'v'Lamadtem.' Only one commanded to learn Torah is commanded to teach. This exempts a woman from teaching her son, and from learning. One must learn only if others must teach him. Others need not teach her, for it says "you will teach your sons", not your daughters.

Sotah 20a (Mishnah - Ben Azai): One must teach his daughter Torah, so if she (is a guilty Sotah and) drinks, she will know that her merit is suspending her death;

R. Eliezer says, one who teaches his daughter Torah, he teaches her Tiflus (folly).

R. Yehoshua says, a woman prefers one Kav of food and Tiflus, to nine Kabim and Perishus (abstention).

21a - Question: Which merit can suspend her death? It cannot be merit of Torah. A woman is not commanded!

Answer (Ravina): It is merit of Torah. True, she is not commanded to learn, but since she brings her sons to learn written Torah and Mishnah, and misses her husband when he is learning, she shares in their reward.

21b: R. Eliezer means that it is as if he teaches her Tiflus.

(R. Avahu): He learns from "I (the Torah) am Chachmah, my neighbor is Ormah (cunning)" - once one learns Chachmah, craftiness enters him. (This is bad for women, who are easily swayed, lest they use it for sin.)

Chachamim expound the verse like R. Yosi bar Chanina, to teach that Torah endures only in one who makes himself Arum (naked, of possessions).

Chagigah 3a (R. Elazar ben Azaryah): Men come to Hakhel (to hear the king read Sefer Devarim) to learn. Women come to hear.

Nedarim 35b (Mishnah): Levi may teach written Torah to the sons and daughters of David, even if a vow forbids David to benefit from Levi.

Rishonim

Rambam (Hilchos Talmud Torah 1:13): A woman who learned Torah gets reward, but less than a man, for she is not commanded. Even so, Chachamim forbade teaching Torah to one's daughter, for most women's minds are not suited for Torah. They exchange words of Torah for words of folly. Teaching her oral Torah (she'Ba'al Peh) is like teaching her Tiflus (Aveirah). One should not teach her written Torah, but doing so is not teaching her Tiflus.

Griz Al Rambam (Hilchos Berachos 11:16): The Rambam (Hilchos Tzitzis 3:9) says that if a woman performs any Mitzvah from which she is exempt without a Berachah, we do not protest. He permits women to say Birkas ha'Torah, for it is not for the Mitzvah, rather, for the Torah itself.

Rashi (Sotah 21b DH k'Ilu and DH Rotzah): Since women disdain abstention, it is not good to teach Torah to them. She will learn how to conceal her deeds.

Tosfos (Chagigah 3a DH Nashim): R. Elazar ben Azaryah taught that women come (only) to hear. The Yerushalmi says that this is unlike Ben Azai, who says that one must teach Torah to his daughter.

Poskim

Shulchan Aruch (OC 47:14): Women bless Birkas ha'Torah.

Source (Beis Yosef DH v'Chosav, citing the Agur): The Maharil (Teshuvos Chodoshos 45) says so. Even though women are exempt, and teaching one's daughter is like teaching her Tiflus, this refers to oral Torah, but not to written Torah. Even though the Berachah "to engage in Divrei Torah' alludes to oral Torah, we do not change the text of Berachos. Also, they bless for reading the Korbanos. Tefilah was enacted corresponding to the Korbanos. They must pray, and therefore must read about the Olah and Korbanos. All the more so they must bless according to Semag (Hagahos Tur ha'Shalem - Semak), who obligates them to learn laws that apply to them.

Rebuttal (Gra 18): The Torah exempts women - "you will teach your sons." not your daughters. How can they say 'Who commanded us' and 'Who gave to us (His Torah)'? Rather, women may bless on Mitzvos from which they are exempt (e.g. an Aseh sheha'Zman Gerama - Tosfos Kidushin 31a DH d'Lo).

Beis ha'Levi (1:6:1): Women do not have merit of their own Talmud Torah (Sotah 21a)! They do not come to Hakhel to learn their Mitzvos (Chagigah 3a)! Semag obligates them to learn what they must do, but it is not a Mitzvah! Rav says that one who omitted Torah in Birkas ha'Mazon was Yotzei, for women are exempt (Berachos 49a)! The Agur permits them to bless, like on Mitzvos from which they are exempt. We do not say that they are forbidden to learn, for they must say Korbanos and learn about their Mitzvos.

Question (against the Agur - Minchas Chinuch Sof 430 DH u'Mevu'ar): Learning to know relevant laws does not obligate Birkas ha'Torah!

Answer (Mishmeres Chaim 2 p.30): We must say that the Agur exempts women from learning laws that do not apply to them, but they are fully commanded about Talmud Torah regarding laws relevant to them.

Drishah (DH v'Chosav): Even a Nochri (who is Chayav Misah for learning Torah) who learns Torah is greater than a Kohen Gadol (Avodah Zarah 3a)! Tosfos explains that this refers to learning Mitzvos relevant to him.

Gra (22): A woman is no worse than a Nochri.

Shulchan Aruch (YD 246:6): A woman who learned Torah gets reward, but not like a man, for she is exempt. Chachamim commanded not to teach Torah to one's daughter, for most women's minds are not suited to Torah. They exchange words of Torah for words of folly. Teaching one's daughter oral Torah is like teaching her Tiflus. One should not teach her written Torah, but this is not Tiflus.

Taz (4): The Tur wrote that teaching to her written Torah is Tiflus, but teaching oral Torah is not. The Beis Yosef said that this is a scribal error; it must say oppositely. A proof for this is Hakhel (women must hear Sefer Devarim). If so, we should teach them written Torah l'Chatchilah! Indeed, we teach women the simple meaning. L'Chatchilah one may not teach deeper understanding. Men come to learn, and women come to hear.

Gra (24,25): We follow R. Eliezer, R. Yehoshua and R. Elazar ben Azaryah against Ben Azai. We learn from Nedarim 35b that teaching written Torah to girls is not Tiflus. The Rambam (Perush ha'Mishnayos and Hilchos Nedarim 6:7) omitted this, for l'Chatchilah we do not teach girls.

Note: The Mishnah permits l'Chatchilah! If it permits only girls whom we know will learn properly, what is the source that teaching Stam girls is not Tiflus?

Birkei Yosef (7): Normally, the Halachah is unlike R. Eliezer. However, R. Elazar ben Azaryah expounded on a Shabbos when he was Nasi. Presumably, the Chachamim were present and accepted it.

Rema: A woman must learn laws relevant to her. She need not teach her son. If she helps her son or husband to learn Torah, she shares their reward.

Gra (26): Tosfos (Sotah 21b DH Ben): The Yerushalmi says that Ben Azai argues with R. Elazar ben Azaryah. I.e. Ben Azai holds that one teaches his daughter only so she will know that merit suspends death, but R. Elazar holds that we teach to women how to fulfill their Mitzvos.