(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.
(25) On the third day, when they were in pain, Simeon and Levi, two of Jacob’s sons, brothers of Dinah, took each man his sword, came upon the city unmolested, and slew all the males.
רש"י- מסכת נזיר כ"ט:
ור' יוסי ברבי יהודה סבר מופלא הסמוך לאיש מדאורייתא. ... שלא מצינו בכל התורה שיהא קרוי איש בפחות מבן י''ג אבל בבן י''ג מצינו שקראו הכתוב איש כדכתיב (בראשית לד) ויקחו שני בני יעקב שמעון ולוי איש חרבו וגמירי שמעון ולוי בההיא שעתא בני י''ג שנה הוו ...
Rashi- Talmud Nazir- 29b
ור' יוסי ברבי יהודה סבר מופלא הסמוך לאיש מדאורייתא
...In the Entire Torah we find that that someone is called a "man" who is less than 13 years old. But once they turn 13, they are called a "man", as it says (Bereshit 34), "...Simeon and Levi, two of Jacob’s sons, brothers of Dinah, took each man his sword...". The Gemarah learns that both Shimon and Levi were 13 at this point...
קָטָן שֶׁהִגִּיעַ לִכְלַל שְׁנוֹתָיו שֶׁנִּרְאוּ בּוֹ סִימָנֵי בַּגְרוּת מִלְּמַעְלָה אֵינוֹ צָרִיךְ בְּדִיקָה. וְאִם לָאו אֵין מְקַבְּלִין עֵדוּתוֹ עַד שֶׁיִּבָּדֵק. וּבֶן שְׁלֹשׁ עֶשְׂרֵה שָׁנָה וְיוֹם אֶחָד שֶׁהֵבִיא שְׁתֵּי שְׂעָרוֹת וְאֵינוֹ יוֹדֵעַ בְּטִיב מַשָּׂא וּמַתָּן אֵין עֵדוּתוֹ עֵדוּת בְּקַרְקָעוֹת מִפְּנֵי שֶׁאֵינוֹ מְדַקְדֵּק בִּדְבָרִים שֶׁהֲרֵי אֵינוֹ יוֹדֵעַ. אֲבָל בְּעֵדוּת מִטַּלְטְלִין מְקַבְּלִין עֵדוּתוֹ הוֹאִיל וְהוּא גָּדוֹל:
A minor who has reached the age when you would see signs of his maturity (puberty) in the upper parts (his face), does not need to be checked (for Pubic hair). If not, we not accept his testimony unless he is checked. When the child turns 13 years and 1 day and has produced 2 hairs and he does not know the ways of business, his testimony and land sales is not accepted as he does not know about these matters. But in other matters of testimony, we accept him as an adult.
הַבַּת שֶׁיָּלְדָה אַחַר שְׁתֵּים עֶשְׂרֵה שָׁנָה אַף עַל פִּי שֶׁלֹּא הֵבִיאָה סִימָנִים לֹא תַּחְתּוֹן וְלֹא עֶלְיוֹן הֲרֵי זוֹ גְּדוֹלָה. בָּנִים הֲרֵי הֵם כְּסִימָנִין:
A girl who has reached 12 years and 1 day, even though she has not yet produced the "lower signs" (menstruation) or the "upper signs" (developed breasts), she is considered an adult. Boy are dependent upon producing signs.
Boys, from the time they are born until they have reached 13 years and 1 day, are called children. Even if they produce several (pubic) hairs during this time, these are not considered signs of their maturity. Once they produce 2 pubic hairs and have reached the age of 13 years and 1 day, the are considered an adult.
פסול סומא וחרש שוטה וקטן. ובו יד סעיפים:
קטן פסול להעיד אפי' היה נבון וחכם עד שיביא שתי שערות אחר י"ג שנים גמורות ואם שהו מלבדקו זמן רב אחר שהיה לו י"ג שנה ובדקוהו ונמצאו לו ב' שערות הוא בחזקת גדול משעה שהיה לו י"ג שנה ואם נתמלא זקנו א"צ בדיקה:
If someone has never met a certain friend, and has only corresponded with them through letters, even though seeing this friend would bring the person much joy, he does not bless (Shehchiyanu) when he sees him. Some say that when the son reaches the age of Bar Mitzvah the father blesses "Bless you God, king of the universe, who has exempted me from the sins of this one". It is better to bless without using God's name.
Bar MItzvah- this is when the boy is 13 years and 1 day. And now, the custom is to not say this blessing until the teenager is now praying in a minyan as the leader, or he reads from the Torah on Shabbat so that many people are aware that he is now the age of Mitzvot. It is a mitzvah for the father to make a meal on the day that son turns Bar Mitzvah just like on the day of the wedding. This takes place on the day he enters his 14th year. And the purpose of the meal is that now he is a "Man" in Israel, who is commanded in the laws of the Torah. And if the Son is learned, he should speak/teach at this meal, even if it is not on the actual day.
(ז) שפטרני מענשו וכו' - פי' דעד עכשיו נענש האב כשחטא הבן בשביל שלא חנכו למצות התורה ועכשיו שנעשה איש מחוייב הוא להתחזק בעצמו למצות הש"י...
"That I am absolved of his sins..." To say, until now, the father 'received' the punishments that the child 'earned' because he did not teach him the ways of the Torah. Now that he is Bar mitzvah, it is up to him to learn the ways...