(ג) נשים ועבדים וקטנים פטורין מקריאת שמע ומן התפילין וחייבין בתפלה ובמזוזה ובברכת המזון:
(3) Women, slaves, and minors are exempt from reciting Shema and from tefillin and are obligated in [reciting] Shemoneh Esrei and in [affixing a] Mezuzah and in [reciting] Birkat HaMazon.
Talmud Bavli
כרבי יוסי דאמר נשים סומכות רשות
In accordance with the opinion of Rabbi Yosei, who said: It is optional for women to place their hands on the head of a sacrificial animal before it is slaughtered. Although only men have this obligation, women may perform that rite if they wish. Similarly, women may perform other mitzvot that they have no obligation to fulfill.
דאי לא תימא הכי אשתו של יונה היתה עולה לרגל ולא מיחו בה מי איכא למ"ד רגל לאו מצות עשה שהזמן גרמא הוא אלא קסבר רשות הכא נמי רשות
As, if you do not say so, that this tanna holds in accordance with the opinion of Rabbi Yosei, the baraita states that Jonah’s wife would ascend to Jerusalem for the Festival pilgrimage and the Sages did not reprimand her. Is there anyone who says that the mitzva of Festival pilgrimage is not a time-bound positive mitzva and that women are obligated to fulfill it? Rather, he holds that she did not embark on the pilgrimage as an obligation, but that it was optional; here, too, with regard to phylacteries, it is optional. Consequently, no proof can be cited from this baraita as to whether or not Shabbat is a fit time for phylacteries.
אלא האי תנא היא דתניא המוצא תפילין מכניסן זוג זוג אחד האיש ואחד האשה אחד חדשות ואחד ישנות דברי ר"מ ר' יהודה אוסר בחדשות ומתיר בישנות
Rather, who is the tanna who maintains that Shabbat is a time for phylacteries? It is this tanna who taught the halakha, as it was taught in the Tosefta: One who finds phylacteries brings them in pair by pair, whether the finder is a man or whether she is a woman, and whether the phylacteries are new or whether they are old. This is the statement of Rabbi Meir. Rabbi Yehuda prohibits bringing in new phylacteries since they might merely be amulets in the form of phylacteries, but he permits bringing in old ones, which are certainly valid phylacteries.
ע"כ לא פליגי אלא בחדשות וישנות אבל באשה לא פליגי שמע מינה מצות עשה שלא הזמן גרמא הוא וכל מצות עשה שאין הזמן גרמא נשים חייבות
Analysis of this Tosefta indicates that Rabbi Meir and Rabbi Yehuda disagree only with regard to the issue of new phylacteries and old ones; however, with regard to a woman bringing in the phylacteries, they do not disagree that it is permitted. Learn from it that this tanna maintains that donning phylacteries is a positive mitzva not bound by time, and since women are obligated in every positive mitzva not bound by time, a woman may don these phylacteries and walk into the town.
נָשִׁים וַעֲבָדִים וּקְטַנִּים פְּטוּרִין מִן הַצִּיצִית מִן הַתּוֹרָה. וּמִדִּבְרֵי סוֹפְרִים שֶׁכָּל קָטָן שֶׁיּוֹדֵעַ לְהִתְעַטֵּף חַיָּב בְּצִיצִית כְּדֵי לְחַנְּכוֹ בְּמִצְוֹת
Women and slaves and children are exempt from fringes from the Torah. But it is from the words of the [rabbis] that every child who knows how to wrap himself is obligated [to wear] fringes, in order to educate him in the commandments.
וְנָשִׁים וַעֲבָדִים שֶׁרָצוּ לְהִתְעַטֵּף בְּצִיצִית מִתְעַטְּפִים בְּלֹא בְּרָכָה. וְכֵן שְׁאָר מִצְוֹת עֲשֵׂה שֶׁהַנָּשִׁים פְּטוּרוֹת מֵהֶן אִם רָצוּ לַעֲשׂוֹת אוֹתָן בְּלֹא בְּרָכָה אֵין מְמַחִין בְּיָדָן
And women and slaves that want to wrap themselves with fringes, may wrap themselves without a blessing. And so [too] other positive commandments that women are exempted from; if they want to do them without a blessing, we do not protest against them.
:טֻמְטוּם וְאַנְדְּרוֹגִינוּס חַיָּבִין בְּכֻלָּן מִסָּפֵק לְפִיכָךְ אֵין מְבָרְכִין אֶלָּא עוֹשִׂין בְּלֹא בְּרָכָה
A tumtum (a person with recessed sexual organs) and an androginos (a person with both male and female sexual organs) are obligated in all [of these commandments] because of a doubt. Therefore, they should not recite a blessing, but rather do them without a blessing.
מתני׳ אין מעכבין את התנוקות מלתקוע אבל מתעסקין עמהן עד שילמדו
MISHNA: One need not prevent children from sounding the shofar on Rosh HaShana, despite the fact that they are not obligated in mitzvot. Rather, one occupies himself with them, encouraging and instructing them, until they learn how to sound it properly.
...And they may recite the blessings over a positive time bound commandment, even though they are example from that mitzvah and they may occupy themselves with that mitzvah like Mikhal bat Kushi who, it can be assumed, also recited the blessing. (Rabbeinu Tam)
Since we established that the Mishnah follows Rabbi Yehudah, while Rabbi Yossi and Rabbi Shimon disagree with it - we reject the Mishnah in favor of the beraita. And all positive time bound commandments, even though they are not obligated [for women], they are a permissible mitzvah, and even if they bless on them "who has sanctified us with His commandments and commanded us" to blow the shofar or to hear [the shofar] or to sit in the sukkah or to wave the lulav, we do not protest, like Mikhal bat Shaul who used to put on tefillin and like pilgrim festivals and the Sages did not protest, as it is wirrten in Chapter Hamotzei Tefillin (Erubin 96a). And thus the ruling has gone forth from before the Sages of this place [=Provence] may their memory be blessed, and from before the Sages of France and they brought proofs for their words at lenghth and they are written in their books of responsa.
(Rabbi Zerahia Halevi)