(These are some of the more problematic texts concerning women. They formed the basis of a Purim Rosh Chodesh meeting one year: What if women write such texts concerning the role of men?)
All positive commandments which are time-bound: men are obligated and women are exempt. But all positive commandments which are not time-bound are binding upon both men and women. All negative commandments, whether time-bound or not time-bound, are binding upon both men and women, excepting, "You shall not round [the side locks], neither shall you mar [the corner of your beard]," and "He shall not defile himself [through contact with] the dead." {Kiddushin 33b]
The reason women are exempt from time-bound positive mitzvot is that a woman is bound to her husband to fulfill his needs. Were she obligated in time-bound positive mitzvot, it could happen that while she is performing a mitzvah, her husband would order her to do his commandment. If she would perform the commandment of the Creator and leave aside his commandment, woe to her from her husband! If she does her husband's commandment and leaves aside the Creator's, woe to her from her Maker! Therefore, the Creator has exempted her from his commandments, so that she may have peace with her husband. [David ben Joseph Abudarham, 14th c, Spain, in Sefer Abundarham, part III, "The Blessing over Fulfilling the Commandments"]
Mishnah: Women, slaves, and minors are exempt from reciting the Shema and from putting on tefillin, but they are subject to the obligations of prayer, mezuzah, and birkhat ha-mazon.
Gemara: That they are exempt from the Shema is self-evident: It is a positive mitzvah which is time-bound. You might say that because it mentions the kingship of heaven it is different. We are therefore told that it is not so. [Berakhot 20a, b]
Our rabbis taught: All are qualified to be among the seven [who receive aliyot to the Torah when it is read], even a minor and a woman, but the Sages said that a woman should not read because of the congregation's honor. [Megillah 23a]
And in a town made up entirely of kohanim, with not a single Israelite, we say that a kohen will read twice and then a women will read, for "All are qualified to among the seven, even a slave and a woman and a minor"... But the rabbis said that a "woman should not read because of the congregation's honor, so how is it that the congregation's honor is suspended? Because of the blemish cast upon the kohanim: lest they say that they are sons of divorcees. [Maharam of Rothenburg, 13th c., Responsa #47]
She had scarcely finished drinking when her face turns green, her eyes protrude and her vines swell, and it is proclaimed: "Remove her that the Temple court not be defiled!" If she possesses merit, it suspends the effect [of the water]: some merit suspends it for one year, some merit for two, and some for three. Hence declared Ben Azzai: A man must teach his daughter Torah so that if she has to drink she may know that the merit suspends the effect. Rabbi Eliezer said: Whoever teaches his daughter Torah teaches her obscenity. Can it enter your mind [that it is actually] obscenity? Rather, read: as though he teaches her obscenity. Rav Abbahu said: What is Rabbi Eliezer's reason? Because it is written: I, wisdom, am present in subtlety [Prov. 8:12], that is, when wisdom enters a man subtlety enters with it. [Sotah 20a, 21b]
A certain lady asked Rabbi Eliezer why the one sin in the case of the golden calf was punished by three deaths. He said to her: "A woman's wisdom is only in her spinning wheel, for it is written, And any woman of wise heat, with her hands she wove [Ex. 35:25]." His son Hyrcanus said to him: "Why did you not give her some proper answer from the Torah? Now you have lost me 300 kur a year in tithe." He said to him: "Let the words of Torah be burnt and not given to women!" When she went out, the students said to him: "This one you got rid of, but what do you answer to us?" [Jerusalem Talmud, Sotah 3:16a]
Greater is the promise made by the Holy One, blessed be God, to women than to men, for it says: "Rise up, you women that are at ease, you confident daughters, listen to my speech." Rav said to Rabbi Hiyyah: Whereby do women gain this merit? By making their sons go to the synagogue to learn and their husbands go to the Bet Midrash to study the teachings of the rabbis, and by waiting for their husbands until they return from the Bet Midrash. [Berakhot 17a]
Mishnah: If a man forbade himself by vow to have intercourse with his wife, Beth Shammai ruled: two weeks [is the maximum]; Bet Hillel ruled: one week. Students may go away to study the Torah, without the permission [of their wives for} thirty days; laborers [for only] one week. The times for conjugal duty prescribed in the Torah are: for men of independence, every day; for laborers, twice a week; for ass-drivers, once a week, for camel-drivers, once in thirty days; for sailors, once in six months. These are the rulings of Rabbi Eliezer.
Rambam (Moses Maimonides) listed 10 classes of persons who are not considered competent to attest or testify: women, slaves, minors, lunatics, the deaf, the blind, the wicked, the contemptible, relatives, and the interested parties. [Yad, Edut 9:1]