Taanit 26b
אמר רבן שמעון בן גמליאל לא היו ימים טובים לישראל כחמשה עשר באב וכיוה"כ שבהן בנות ירושלים יוצאות בכלי לבן שאולין שלא לבייש את מי שאין לו כל הכלים טעונין טבילה ובנות ירושלים יוצאות וחולות בכרמים ומה היו אומרות בחור שא נא עיניך וראה מה אתה בורר לך אל תתן עיניך בנוי תן עיניך במשפחה (משלי לא, ל) שקר החן והבל היופי אשה יראת ה' היא תתהלל ואומר (משלי לא, לא) תנו לה מפרי ידיה ויהללוה בשערים מעשיה וכן הוא אומר (שיר השירים ג, יא) צאינה וראינה בנות ציון במלך שלמה בעטרה שעטרה לו אמו ביום חתונתו וביום שמחת לבו ביום חתונתו זה מתן תורה וביום שמחת לבו זה בנין בית המקדש שיבנה במהרה בימינו:

The mishna cites a passage that concludes its discussion of the month of Av, as well as the entire tractate of Ta’anit, on a positive note. Rabban Shimon ben Gamliel said: There were no days as joyous for the Jewish people as the fifteenth of Av and as Yom Kippur, as on them the daughters of Jerusalem would go out in white clothes, which each woman borrowed from another. Why were they borrowed? They did this so as not to embarrass one who did not have her own white garments. All the garments that the women borrowed require immersion, as those who previously wore them might have been ritually impure. And the daughters of Jerusalem would go out and dance in the vineyards. And what would they say? Young man, please lift up your eyes and see what you choose for yourself for a wife. Do not set your eyes toward beauty, but set your eyes toward a good family, as the verse states: “Grace is deceitful and beauty is vain, but a woman who fears the Lord, she shall be praised” (Proverbs 31:30), and it further says: “Give her the fruit of her hands, and let her works praise her in the gates” (Proverbs 31:31). And similarly, it says in another verse: “Go forth, daughters of Zion, and gaze upon King Solomon, upon the crown with which his mother crowned him on the day of his wedding, and on the day of the gladness of his heart” (Song of Songs 3:11). This verse is explained as an allusion to special days: “On the day of his wedding”; this is the giving of the Torah through the second set of tablets on Yom Kippur. The name King Solomon in this context, which also means king of peace, is interpreted as a reference to God. “And on the day of the gladness of his heart”; this is the building of the Temple, may it be rebuilt speedily in our days.

Bava Batra 121

תנן התם אמר רבן שמעון בן גמליאל לא היו ימים טובים לישראל כחמשה עשר באב וכיום הכפורים שבהן בנות ירושלים יוצאות בכלי לבן שאולין שלא לבייש את מי שאין לו בשלמא יום הכפורים יום סליחה ומחילה יום שנתנו בו לוחות אחרונות אלא חמשה עשר באב מאי היא

§ The Gemara discusses a mishna that addresses the issue of inter-tribal marriages. We learned in a mishna there (Ta’anit 26b): Rabban Shimon ben Gamliel said: There were no days as joyous for the Jewish people as the fifteenth of Av and as Yom Kippur, as on these days the daughters of Jerusalem would emerge in white garments, which each woman borrowed from another. Why did they borrow garments? They did this so as not to embarrass one who did not have her own white garments. The Gemara analyzes the mishna: Granted that Yom Kippur is a day of joy, because it is a day of pardon and forgiveness, and moreover, it is the day on which the last Tablets of the Covenant were given. But what is the special joy of the fifteenth of Av?

אמר רב יהודה אמר שמואל יום שהותרו שבטים לבא זה בזה מאי דרוש (במדבר לו, ו) זה הדבר דבר זה לא יהא נוהג אלא בדור זה
Rav Yehuda says that Shmuel says: This was the day when the members of different tribes were permitted to marry into one another’s tribe. Such marriages were restricted for the first generation to enter Eretz Yisrael, as discussed above (120a). What verse did the sages of that time interpret in support of their conclusion that this halakha was no longer in effect? The verse states: “This is the matter” (Numbers 36:6), meaning, this matter shall be practiced only in this generation, in which Eretz Yisrael is being divided among the tribes.
רבה בר בר חנה אמר רבי יוחנן יום שהותר שבט בנימן לבא בקהל דכתיב (שופטים כא, א) ואיש ישראל נשבע במצפה לאמר איש ממנו לא יתן בתו לבנימן לאשה מאי דרוש ממנו ולא מבנינו
Rabba bar bar Ḥana says that Rabbi Yoḥanan offered another explanation: The fifteenth of Av was the day when the tribe of Benjamin was permitted to enter into the congregation of the other tribes of Israel through marriage, after the other tribes found a way to dissolve the vow that had prohibited them from marrying a member of the tribe of Benjamin in the aftermath of the episode of the concubine in Gibeah (Judges, chapters 19–20). As it is written: “And the men of Israel had taken an oath in Mizpah, saying: None of us shall give his daughter to Benjamin as a wife” (Judges 21:1). The Gemara asks: What verse did the sages of that time interpret that enabled them to dissolve this vow? The verse states: “None of us,” and not: None of our children; therefore, the oath applied only to the generation that had taken the oath.
רב דימי בר יוסף אמר רב נחמן יום שכלו בו מתי מדבר דאמר מר עד שלא כלו מתי מדבר
Rav Dimi bar Yosef says that Rav Naḥman says: The fifteenth of Av was the day on which those designated to perish in the wilderness stopped dying, as the entire generation that had left Egypt had died due to the sin of the spies (Numbers 14:29–30). As the Master says: As long as those designated to perish in the wilderness had not stopped dying,
לא היה דיבור עם משה שנאמר (דברים ב, טז) ויהי כאשר תמו כל אנשי המלחמה למות מקרב העם וסמיך ליה וידבר ה' אלי לאמר אלי היה הדיבור
God did not speak with Moses, as it is stated: “So it came to pass, when all the men of war were consumed and dead from among the people” (Deuteronomy 2:16), and juxtaposed to that verse it is written: “That the Lord spoke to me, saying” (Deuteronomy 2:17). Moses indicates: Only after the last of that generation had died, was the speech of God directed to me. When the Jewish people realized that the decree had been lifted, the day was established as a permanent day of rejoicing.
עולא אמר יום שביטל בו הושע בן אלה פרדסאות שהושיב ירבעם על הדרכים שלא יעלו ישראל לרגל
The Gemara continues to cite explanations for the significance of the fifteenth of Av. Ulla says: The fifteenth of Av was the day when King Hoshea, son of Ela, removed the guards [pardesaot] that Jeroboam, son of Nevat, placed on the roads so that Israel would not ascend to Jerusalem for the pilgrimage Festival. By doing so, King Hoshea renewed the access to Jerusalem for pilgrims.
רב מתנה אמר יום שנתנו הרוגי ביתר לקבורה דאמר רב מתנה אותו היום שנתנו הרוגי ביתר לקבורה תקנו ביבנה הטוב והמטיב הטוב שלא הסריחו והמטיב שנתנו לקבורה
Rav Mattana says: The fifteenth of Av was the day when the slain victims of Beitar were afforded burial, several years after they were killed and the Roman emperor Hadrian decreed that they were not to be buried (see Gittin 57a). As Rav Mattana says: On the day that the slain of Beitar were afforded burial, the Sages in Yavne instituted the blessing: Blessed is He Who is good and Who does good. The term: Who is good, is to give thanks that the corpses did not decompose despite the long delay; and the term: And Who does good, is to give thanks that the slain ones were ultimately afforded burial.
רבה ורב יוסף דאמרי תרוייהו יום שפוסקין בו מלכרות עצים למערכה תניא רבי אליעזר הגדול אומר כיון שהגיע חמשה עשר באב תשש כחה של חמה ולא היו כורתין עצים למערכה אמר רב מנשה וקרו ליה יום תבר מגל
Rabba and Rav Yosef both say: The fifteenth of Av is the day when they stop cutting wood for the arrangement of wood on the altar. It is taught in a baraita that Rabbi Eliezer the Great says: Once the fifteenth of Av came, the force of the sun would weaken, and from this date they would not cut additional wood for the arrangement, because wood cut from then on would not dry properly and would be unfit for use in the Temple. Rav Menashe said: And the people called the fifteenth of Av: The day of the breaking of the sickle [maggal ], as they did not need the lumbering tools until the following year.
Rashi

שכלו מתי מדבר - דתניא כל ארבעים שנה שהיו במדבר בכל ערב תשעה באב היה הכרוז יוצא ואומר צאו לחפור והיה כל אחד ואחד יוצא וחופר לו קבר וישן בו שמא ימות קודם שיחפור ולמחר הכרוז יוצא וקורא יבדלו חיים מן המתים וכל שהיה בו נפש חיים היה עומד ויוצא וכל שנה היו עושין כן ובשנת ארבעים שנה עשו ולמחר עמדו כולן חיים וכיון שראו כך תמהו ואמרו שמא טעינו בחשבון החדש חזרו ושכבו בקבריהן בלילות עד ליל חמשה עשר וכיון שראו שנתמלאה הלבנה בט"ו ולא מת אחד מהם ידעו שחשבון חדש מכוון וכבר מ' שנה של גזרה נשלמו קבעו אותו הדור לאותו היום יו"ט:

1 "[the day] on which the deaths ceased in the desert" - As it was taught in a braita, all 40 years that they were in the desert, every Erev Tisha B’av, the proclaimer would go out and say: let each individual go out and dig [his grave]. And every single person would go out and dig for themselves a grave, and sleep in it, in case they would die before they had dug. And the next day, the proclaimer would go out and proclaim: let the living separate themselves from the dead. And every one who had the soul of life would rise and go out [of his grave]. And every year they would do this. And in the 40th year, they did it, and the next morning everyone stood up alive. And when they saw this, they were astonished, and they said, ‘perhaps we made a mistake in calculating the month [and it is not yet Tisha B’Av].’ They returned and slept in their graves each night until the 15th, and since they saw that the moon was full on Tu [B’av] and no one had died among them, they knew that the calculation of the month was in line, and that the 40 years of the decree had been completed, they established that day as a Yom Tov.

Kitzur Shulchan Aruch
אֵין אוֹמְרִים תַּחֲנוּן לֹא בְּרֹאשׁ חֹדֶשׁ וְלֹא בַּחֲמִשָּׁה עָשָׂר בְּאָב, וְלֹא בַּחֲמִשָּׁה עָשָׂר בִּשְׁבָט וְלֹא בַּחֲנֻכָּה וְלֹא בְּפוּרִים גָּדוֹל בּ' יָמִים, וְלֹא בְּפוּרִים קָטָן בּ' יָמִים, וְלֹא בּל"ג בָּעֹמֶר, וְלֹא בְּכָל חֹדֶשׁ נִיסָן, וְלֹא בְּתִשְׁעָה בְּאָב, וְלֹא בַּיָּמִים שֶבֵּין יוֹם כִּפּוּר לְסֻכּוֹת, וְלֹא מֵרֹאשׁ חֹדֶשׁ סִיוָן עַד לְאַחַר אִסְרוּ חַג דְּשָׁבוּעוֹת וְלֹא בְּאִסְרוּ חַג דְּסֻכּוֹת, בְּכָל אֵלּוּ אֵין אוֹמְרִים בְּמִנְחָה שֶׁלִּפְנֵיהֶם, אֲבָל בְּעֶרֶב רֹאשׁ הַשָּׁנָה וּבְעֶרֶב יוֹם הַכִּפּוּרִים אוֹמְרִים בַּמִנְחָה שֶׁלִּפְנֵיהֶם. וּבְעֶרֶב רֹאשׁ הַשָּׁנָה אוֹמְרִים גַּם בַּסְּלִיחוֹת רַק לְאַחַר כָּךְ אֵין אוֹמְרִים.

Tachanun is not said on the following days: Rosh Chodesh, the fifteenth of Av,13At one time observed as a festival for the numerous wonderful events of this day: 1) The day that God’s decree that 600,000 of those that came into the wilderness shall die before the Jews enter Eretz Yisrael, ended. 2) The day that it became permissible for Jewish women to marry into other tribes of Israel (see Numbers 36:6–9). Also it was the day that the Tribe of Benyamin was again permitted to intermarry with the other tribes of Israel, after being ostracized for a period of time. 3) Jerobaam, the king, had posted soldiers for many years not allowing the Jews their pilgrimages to Jerusalem for the Three Festivals. Hosea, King of Israel, opened the roads to Jerusalem on Av 15. 4) When the Second Temple was completed the land was totally desolate, so much so, that no wood could be found for burning on the Altar. Many Jews jeopardized their lives and disobeyed the authorities and brought wood for the Altar. The day when cutting this wood was completed was Av 15