Since the Beis HaMikdash was destroyed on account of undeserved hatred, this reason must be undone by means of unearned love -- by loving every Jew without cause, even when one sees no apparent justification for loving him.
This is the inner meaning of the teaching of our Sages that "Pinchas is Eliyahu." Pinchas epitomizes peace and unity, as in the Divine promise, "I hereby grant him My covenant of peace." And it is this unity which will bring the Prophet Eliyahu, the harbinger of the Redemption.
Likkutei Sichos, Vol. II, p. 598
A Letter in a Sefer Torah
The obligation to write a Sefer Torah is the culmination of all the 613 mitzvos (as in the Sefer HaChinuch, mitzvah 613). It is thus clear that acquiring a letter in one of the universal Torah scrolls now being written hastens the culmination of the exile.
On this, see Ben Ish Chai on Parshas Bereishis, p. 7.
Likkutei Sichos, Vol. XXIV, p. 215
The Redemption will unify all of Israel, from the greatest to the smallest. For not a single Jew will remain in exile: "You, the Children of Israel, will be gathered in one by one." Moreover, the multitudes who will then be gathered in are described collectively, in the singular: "A great congregation will return here."
In preparation for this state, therefore, one should make every endeavor to unify all the different kinds of Jews, in a spirit of ahavas Yisrael, the love of a fellow Jew, and of achdus Yisrael,the unity of all Israel.
From a talk of the Rebbe on the eve of the Fifth Day of Sukkos, 5745 
Our Sages teach, "By virtue of faith, our forefathers were redeemed from Egypt."
Our future Redemption will likewise come about by virtue of the fact that our people, disregarding the thick darkness of our present exile, believe firmly in the imminent coming of Mashiach.
Likkutei Sichos, Vol. III, p. 872
By Virtue of Pious Women
"By virtue of the pious women of that generation, our forefathers were redeemed from Egypt."
In the same way, the future Redemption will come about by virtue of the spiritual labors of Jewish women and girls.
We therefore see that the three particular mitzvos which have been entrusted to Jewish women and girls -- lighting candles in honor of Shabbos and Yom-Tov, separating the tithe ofchallah from bread and baked goods, and the family purity laws -- all involve needs which are basic to all of humanity, including gentiles (viz., light, food, and family life). It is the task of Jewish women and girls to ensure that these activities be undertaken in a distinctively Jewish manner, highlighting the connection of the candle-lighting with Shabbos and Yom-Tov; thekashrus of the family's food and drink; and the purity of the family.
These labors constitute a preparation for the coming of Mashiach, when the very materiality of the world will be refined. As it is written concerning that era, "And all flesh will together see that the mouth of G-d has spoken."
Likkutei Sichos, Vol. XX, p. 227
Printing the Tanya
Since in the future Redemption not a single Jew will remain in exile, it is clear that the redemption of every individual Jew has a bearing on the Redemption of the entire House of Israel. It is thus our duty to work with every Jew to ensure that he will be ready for the Redemption.
This is accomplished by disseminating the Torah and especially its pnimiyus, its innermost and mystical dimension, wherever Jews are to be found, and wherever even only one single Jew is to be found.
Therefore, in order that the wellspring itself (and not merely the waters that derive from it) should reach the furthermost places (chutzah), the Tanya should be printed everywhere, for it is the Written Law of the teachings of Chassidus. The wellspring itself, the source of the life-giving waters, will thus be found in every such place.
From a talk of the Rebbe on Shabbos Parshas Terumah, 5744 
1. Yoma 9b.
2. Targum Yonasan on Shmos 4:13.
3. Bamidbar 25:12.
4. Yeshayahu 27:12.
5. Yirmeyahu 31:7.
6. Mechilta on Shmos 14:31.
7. Sotah 7b.
8. Yeshayahu 40:5.
9. See the above passage entitled "When Your Wellsprings Will Be Disseminated Outward" (p. 71).
10. In the original, "Torah shebichsav."