At the close of the Tractate Ta'anis the Mishnah describes the holiday of the 15th of Av:
There never were in Israel greater days of joy than the 15th of Av and the day of Yom Kippur. On these days the daughters of Yerushalayim used to walk out in white garments which they borrowed in order not to put to shame anyone who had none...and danced in the vineyards. (Ta'anis 26b)
The reasons for this unique holiday are listed in the Gemara:
It is the day on which permission was granted to the tribes to intermarry.... It is the day on which the generation of the wilderness ceased to die out.... It is the day on which Hoshea the son of Ellah removed the guards which Yeravam the son of Nevat had placed on the roads to prevent Israel from going up to Yerushalayim for the pilgrimage.... It is the day when permission was granted to bury those killed at Betar.... It is the day on which they discontinued to fell trees for the altar. (Ibid. 30b-31a)
It is obvious that the observance of this holiday could only take place when the Beis HaMikdash still existed and there were a "daughter of the Kohen Gadol" and a "daughter of the king." It was also necessary that there be independence and peace in Jerusalem.
Nevertheless, since the Torah is eternal and must be observed in all places, one may suppose that even in the diaspora we should remember and relive this holiday in such a manner as to relate it to our own Divine service and action.
In addition to the spiritual analogy which we draw from the 15th of Av the Gemara also mentions one aspect of this day which applies to action. Since the nights become visibly longer after the 15th of Av the Gemara tells us to increase our Torah learning which will add years to our lives. Similarly, the Shulchan Aruch rules that from the 15th of Av we must increase our Torah learning little by little, every day.
Why is the 15th of Av seen as such a glorious holiday?
Pesach and Sukkos are also celebrated on the 15th of the month, when the moon is in its full state, yet the 15th of Av is rated much higher because it represents the ascent to fullness that follows the worst descent of the year as exemplified by the 9th of Av. The extreme nadir of Tisha B'Av is, after all, for the purpose of rising to a higher state and the 15th of Av represents that supreme ascent. This is explained by the Midrash:
The lion rose in the constellation of the lion and destroyed Ariel (the Beis HaMikdash)...on condition that the lion will come in the constellation of the lion and rebuild the Beis HaMikdash. (Yalkut, Yermiyahu #259)
Since every elevation is relative to the preceding fall, it follows that the ascent of the 15th of Av is the greatest of them all.
This down and up movement in accordance with the waxing moon is closely associated with the Jewish people who are compared to the moon. So, on Tisha B'Av we commemorate the destruction of the Temples and the dispersion of the Jewish people which is on condition that afterwards we will attain the loftiest elevation of the 15th of Av. Since Tisha B'Av is so intense a day of sadness it then follows that there were no greater days of joy than the 15th of Av.
In the same vein the reasons given in the Gemara for the festive mood of the 15th of Av will also represent opposite situations and rectification for the shortcomings of Tisha B'Av.
The terrible decree that the generation of the desert would all die in the desert was issued on Tisha B'Av. Each year, the Midrash describes, the Jews in the wilderness would dig graves on the eve of the 9th of Av...some would perish and some would survive. But on the year of the annulment of the decree they all rose -- alive. At first they thought they had erred in the date -- but on the night of the 15th of Av, when the moon shone in its fullness, they knew that the decree had been abolished so they proclaimed the day a holiday. The full moon of the 15th of Av rectified and refined the decree of Tisha B'Av.
Likewise, the other reasons listed in the Gemara all exemplify the attribute of Ahavas Yisrael which is the antidote to the unwanted hatred that precipitated the destruction. The tribes could intermarry again, the martyrs of Betar could be buried, these are examples of Ahavas Yisrael. The elimination of the boarder guards by Hoshea ben Ellah, so that the Jews of the Northern Kingdom could once again go to Yerushalayim for the pilgrimage, this too brought Ahavas Yisrael. As the Gemara says, the pilgrimage to Yerushalayim brought brotherhood and friendship among the Jewish people.
The preparation of logs for the fire on the Altar was also an act of kindness and charity that extended itself to all the Jewish people, for it made the fire on which all offerings were sacrificed, including those of individuals.
We may also discern this theme of Ahavas Yisrael in the practice of the 15th of Av when the daughters of Tziyon would borrow dresses and go out to dance in the orchards.
All class status was forgotten and all the girls danced together. Everyone had to borrow a dress -- so that no one was shamed and each had to ask a friend for a favor, the epitome of unity and love.
Our eternal lesson: we must experience overwhelming joy on this day, for we reach the apex of ascent and the rectification of loss following the nadir of descent on Tisha B'Av, it is therefore above all the other holidays. We must express these emotions by strengthening our Divine service, devoted to the nullification of the cause of the golus -- namely "Because of our sins were we exiled." How? through Ahavas Yisrael and Jewish unity.
It has therefore become an accepted custom to gather on the 15th of Av and celebrate by strengthening our unity and love which increases the correction of the causes of the exile. This is all connected with the spiritual themes of the 15th.
As to the Gemara's ruling about Torah learning, that is a practical directive which applies to us because the essence and life-force of the Jew is Torah. Therefore the ascent of the 15th of Av which is dependent on the waxing moon and represents the ascent of the life of the Jewish people -- expresses itself and is related to Torah and the light of Torah which is "our life and the length of our days."
Furthermore, in speaking of the forces of consolation and renewal the prophet tells us, "Tziyon will be redeemed with justice and her returnees with charity." (Yeshayahu 1:27) Here is a direct reference to Torah (justice). So Torah emerges as the essential theme of the 15th of Av for it will correct the downfall of Tisha B'Av.
For this reason the Mishnah quotes the verse from Shir HaShirim: "Go forth daughters of Tziyon and gaze upon King Shlomo...the crown with which his mother crowned him..." (Shir HaShirim 3:2) -- which calls the daughters of Tziyon to go out and see the crown of Shlomo -- referring to the day of Mattan Torah. Clearly, this reference to the day of Mattan Torah is a reference to Torah study which is clearly associated with the 15th of Av.
Now we may perceive how the Holy One, Blessed be He, established the nature of the world that after the 15th of Av the nights are visibly longer. Why is this so in nature? because the spiritual purpose of night is for Torah study and since the 15th of Av begins a new cycle of renewal and a new order is set in motion, similar to Mattan Torah, therefore, nature too, conforms to the cycles of Torah.
We must glean a practical lesson in our Divine service, which justifies that we have in fact heard and learned the subject properly. On this 15th of Av we must start a new order in Torah study. As the night grows longer so, too, must our Torah learning increase qualitatively and quantitatively. Each individual according to his/her own ability should make a sincere resolution to undertake a new subject to study, join a new class, learn a new field, a new book or a new part of Torah -- all infused with a new enthusiasm -- a qualitative increase. Do not be satisfied with a general resolution, state immediately what book or subject you are accepting.
"Study is great for it leads to action" thus, these resolutions for greater study will bring new enthusiasm in pious and devoted observance of mitzvos. Starting with Ahavas Yisrael and Jewish unity and a special increase in charity. If possible it would be praiseworthy to connect the increase in Torah with tzedakah so as to bring the realization of the prophecy: "Tziyon will be redeemed with justice (Torah) and his returnees with charity." Being a Shemittah year, we are given more power to bring these resolutions to reality. Being exempt from working in the fields we are prompted to devote our time "to seek G-d" by studying Torah. The Shemittah year also serves as a preparation for the Hakhel year when all Jews will gather to hear the words of Torah:
You must gather together the people, the men, women, children...and let them hear it. They will thus learn to be in awe of G-d your L-rd, carefully keeping all the words of this Torah. (Devorim 31:12)
It is appropriate that the resolutions should be accepted publicly, which will incorporate greater power for success. Let those who hear my voice now, here in the synagogue of the Previous Rebbe, and all over the world, accept the good resolutions now. So, too, in all places may the good actions begin before this Shabbos, the 20th of Av, which is connected to the 15th by virtue of it also being a day of wood donations. (Ta'anis 26a) On Shabbos all the days of the week also reach elevation and perfection.
But these commitments should not be enough, rather, each month in the future everyone should make a self-evaluation and see where there might be room for further improvement. Talk it over with another -- "Make yourself a teacher."
Commensurate with your new system of learning, conform and increase your Torah and tzedakah.
Every Jew must study Torah, "our life and the length of our days," and so this applies to everyone and you should endeavor to spread the word far and wide, as much as possible.
In order to enhance and increase your success it is advisable to write down your resolutions regarding the increase in Torah, tzedakah and mitzvos. These notes should be submitted so that they may be transmitted to the graveside of the Previous Rebbe.
May G-d help everyone fulfill their commitments so that it will be even easier to carry them out than imagined.
And may these increases engender the complete redemption through our righteous Moshiach and then the Third Beis HaMikdash will be built speedily in our time, may we rejoice and celebrate in the salvation.