(כא) הוּא הָיָה אוֹמֵר, בֶּן חָמֵשׁ שָׁנִים לַמִּקְרָא, בֶּן עֶשֶׂר לַמִּשְׁנָה, בֶּן שְׁלשׁ עֶשְׂרֵה לַמִּצְוֹת, בֶּן חֲמֵשׁ עֶשְׂרֵה לַתַּלְמוּד, בֶּן שְׁמֹנֶה עֶשְׂרֵה לַחֻפָּה, בֶּן עֶשְׂרִים לִרְדֹּף, בֶּן שְׁלשִׁים לַכֹּחַ, בֶּן אַרְבָּעִים לַבִּינָה, בֶּן חֲמִשִּׁים לָעֵצָה, בֶּן שִׁשִּׁים לַזִּקְנָה, בֶּן שִׁבְעִים לַשֵּׂיבָה, בֶּן שְׁמֹנִים לַגְּבוּרָה, בֶּן תִּשְׁעִים לָשׁוּחַ, בֶּן מֵאָה כְּאִלּוּ מֵת וְעָבַר וּבָטֵל מִן הָעוֹלָם:
(21) He used to say: At five years of age the study of Scripture; At ten the study of Mishnah; At thirteen subject to the commandments; At fifteen the study of Talmud; At eighteen the bridal canopy; At twenty for pursuit [of livelihood]; At thirty the peak of strength; At forty wisdom; At fifty able to give counsel; At sixty old age; At seventy fullness of years; At eighty the age of “strength”; At ninety a bent body; At one hundred, as good as dead and gone completely out of the world.
(ח) מִי שֶׁנַּעֲשָׂה בְּנוֹ בַּר מִצְוָה, כְּשֶׁעוֹלֶה לַתּוֹרָה בַּפַּעַם הָרִאשׁוֹנָה, לְאַחַר שֶׁבֵּרַךְ בְּרָכָה אַחֲרוֹנָה עַל סֵּפֶר הַתּוֹרָה, מְבָרֵךְ הָאָב וְאוֹמֵר, בָּרוּךְ אַתָּה ה' אֱלֹקֵינוּ מֶלֶךְ הָעוֹלָם, אֲשֶׁר פְּטָרַנִי מֵעָנְשׁוֹ שֶׁל זֶה (עַיֵּן בספר חיי"א). וּמִצְוָה עַל הָאָדָם לַעֲשׂוֹת סְעוּדָה בְּיוֹם שֶׁנַּעֲשָׂה בְּנוֹ בַּר מִצְוָה, דְּהַיְנוּ בְּיוֹם שֶׁנִּכְנַס לִשְׁנַת הָאַרְבַּע עֶשְׂרֵה. וְאִם הַנַּעַר דּוֹרֵשׁ, הֲוֵי סְעוּדַת מִצְוָה אֲפִלּוּ אֵינָהּ בְּאוֹתוֹ יוֹם (רכה).
(8) The first time a Bar Mitzvah is called to the Torah, after he has concluded the second berachah over [the reading of] the Torah, the father says the following berachah: Baruch ata Adonoy Elokeinu melech ha'olam asher petarani mei'onsho shel zeh [Blessed are You, Hashem, our God, King of the universe Who has freed me from the punishment due this boy]. It is a mitzvah for a father to prepare a festive meal on the day that his son becomes Bar Mitzvah, that is, on the first day of his fourteenth year. If the boy delivers a Torah discourse, it is considered a meal for the sake of a mitzvah even if [the banquet] is not given on the [Bar Mitzvah] day.
(ב) הגה יש אומרים מי שנעשה בנו בר מצוה יברך בא"י אמ"ה שפטרני מעונשו של זה (מהרי"ל בשם מרדכי ובר"ר פ' תולדות) וטוב לברך בלא שם ומלכות (דעת עצמו):
Rama: one who's son reaches BM should say the following bracha...Some say it should be said without בא"י אמ"ה (i.e. do not actually say Hashem's name)
Kaf Hachaim
The Bar Mitzvah boy should try to learn as much as possible on the day of his Bar Mitzvah. Preferably, he should learn Mishnayos.
Chinuch Yisrael
Most Poskim say he becomes Bar Mitzvah 13 years after the day he was born at Tzes Hakochavim (not at the time that he was born).
Kaf Hachaim
The Bar Mitzvah boy should wear new clothes or eat a new fruit and while saying the Shehechyanu should have in mind to also be making the bracha on his new acceptance of the mitzvos
Rav Moshe Feinstein
While having a bar mitzvah party celebrates the change that comes to a man (he can now be in a minyan, beis din, etc.), the idea of a bas mitzvah comes from the outside world. While it is not assur to celebrate a bas mitzvah, it should be seen as a birthday party and one should not make a big deal out of it.
Rav Ovadia Yosef
Although there is no real custom for it, a bas mitzvah girl may have a celebration to show her happiness in becoming obligated in Torah and Mitzvos, just like a bar mitzvah boy.