Halakhah zu Sotah 3:4
אֵינָהּ מַסְפֶּקֶת לִשְׁתּוֹת עַד שֶׁפָּנֶיהָ מוֹרִיקוֹת וְעֵינֶיהָ בּוֹלְטוֹת וְהִיא מִתְמַלֵּאת גִּידִין, וְהֵם אוֹמְרִים הוֹצִיאוּהָ הוֹצִיאוּהָ, שֶׁלֹּא תְטַמֵּא הָעֲזָרָה. אִם יֶשׁ לָהּ זְכוּת, הָיְתָה תוֹלָה לָהּ. יֵשׁ זְכוּת תּוֹלָה שָׁנָה אַחַת, יֵשׁ זְכוּת תּוֹלָה שְׁתֵּי שָׁנִים, יֵשׁ זְכוּת תּוֹלָה שָׁלשׁ שָׁנִים. מִכָּאן אוֹמֵר בֶּן עַזַּאי, חַיָּב אָדָם לְלַמֵּד אֶת בִּתּוֹ תוֹרָה, שֶׁאִם תִּשְׁתֶּה, תֵּדַע שֶׁהַזְּכוּת תּוֹלָה לָהּ. רַבִּי אֱלִיעֶזֶר אוֹמֵר, כָּל הַמְלַמֵּד אֶת בִּתּוֹ תוֹרָה, כְּאִלּוּ מְלַמְּדָהּ תִּפְלוּת. רַבִּי יְהוֹשֻׁעַ אוֹמֵר, רוֹצָה אִשָּׁה בְקַב וְתִפְלוּת מִתִּשְׁעָה קַבִּין וּפְרִישׁוּת. הוּא הָיָה אוֹמֵר, חָסִיד שׁוֹטֶה, וְרָשָׁע עָרוּם, וְאִשָּׁה פְרוּשָׁה, וּמַכּוֹת פְּרוּשִׁין, הֲרֵי אֵלּוּ מְכַלֵּי עוֹלָם:
Sie trinkt kaum zu Ende, bevor ihr Gesicht grün wird, ihre Augen sich ausbeulen und sie mit Sehnen (oder "Venen") gefüllt zu sein scheint, und sie [die Priester] sagen: "Entferne sie, entferne sie!" so beschmutzt sie den Hof nicht. Wenn sie Verdienst hat, würde es [die oben beschriebenen Effekte] für sie ausgesetzt. Es gibt Verdienste, die für ein Jahr ausgesetzt sind, es gibt Verdienste, die für zwei Jahre ausgesetzt sind, es gibt Verdienste, die für drei Jahre ausgesetzt sind. Von hier aus sagt Ben Azai: Ein Mann ist verpflichtet, seine Tochter Tora zu unterrichten, denn wenn sie [als mutmaßliche Ehebrecherin] trinkt, wird sie wissen, dass das Verdienst es für sie aufhebt. Rabbi Eli'ezer sagt: Wer seine Tochter Tora lehrt, wird so betrachtet, als ob er ihre Dummheit lehrte. Rabbi Yehoshua sagt: Eine Frau wünscht sich ein Kav und Dummheit mehr als neun Kavs und Abstinenz. Er würde sagen: Ein törichter frommer Mann, ein gerissener böser Mann, eine [übermäßig] abstinente Frau und die Selbstgeißelung der Asketen, all dies zerstören die Welt.
Peninei Halakhah, Women's Prayer
However, a woman who wants to learn on her own, not because her parents or institutional context obligates her, may do so. It is even a credit to her, as Rambam says (ad loc.): “A woman who learned Torah receives rewards, but not the same as a man’s reward, as she was not commanded, and whoever performs an action that he is not commanded to perform is not rewarded like one who was commanded. Rather it is less.” It seems, therefore, that the entire prohibition is for a father to initiate Torah study with his daughter; but if she herself is interested in doing so for heaven’s sake, there is no prohibition; on the contrary, she is rewarded. Likewise, Rambam explains (MT, Laws of Torah Principles 4:14) every single person has a mitzva to love God and fear Him. The way one achieves total love and fear for God is through Torah study, initially by studying talmudic debates and knowing what is permitted and what prohibited, and later through the study of the esoteric “work of creation” (“ma’aseh bereishit”) and “work of the chariot” (“ma’aseh merkava”). Concerning this, Rambam writes: “These are the greatest good that God bestowed on the civilized world so that it may inherit the World to Come; and it is possible that everyone understands them – adult and minor, man and woman, one whose mind is expansive as well as one with limited knowledge…” (R. Rabinovitch writes this as well in his commentary on MT, Yad Peshuta). It seems, therefore, that the future ideal of a world filled with the knowledge of God where is one where all women study Torah of their own volition and with complete understanding, thereby arriving at the love and fear of God in its totality. As we know, in the past there were women prophets and sages. However, it seems that even in the ideal there is a difference between the character of men’s and women’s learning.
In summary, a woman whose heart is set on in-depth Torah study may engage in it, and it is to her credit. Still, good and righteous women who have no desire for this type of study should not be taught, and if one does teach them, it is as if he has taught them frivolity. It seems that the reason for this is twofold. One aspect pertains to the feminine nature, which makes it appropriate that she delve into Torah study out of her own desire and freedom. The second reason is that for most women, during the time that the domestic yoke is great and there is very little leisure time, theoretical Torah study cannot be undertaken properly. This makes it like frivolity, and the damage caused by this learning is greater than the benefit gained.
All of this applies solely to theoretical study. Women are obligated to study Torah in order to perform mitzvot (Rema YD 246:6, based on Agur and Smak). Therefore, SA 47:14 rules that women must recite Birkhot Ha-Torah, since women must learn what is necessary for them to live a life of Torah. Today, it is apparent that women need to learn halakha and its reasons, along with the fundamentals of faith, for without this learning, their religious lives would certainly not be on the appropriate level. Therefore, it is an obligation to teach girls however much is necessary in order for them to uphold the Torah and become settled in their faith.