The primary goal in creating Adam was to bring forth King David and his descendants, the main one being Moshiach-He should come speedily in our days. This is hinted at in the acrostic for the Hebrew word Adam: "alef" for Adam, "dalet" for David and "mem" for Moshiach. The main purpose of creation was for the generation of Moshiach.
(Rabbi Shalom of Belz, the Sar Shalom)
(L'Chaim)

The belief in the future Redemption is part of the belief "I am the L-rd your G-d," which is included in the first and foremost of the Ten Commandments. Concerning the belief in G-d... we find that at times we are involved and speak about it. However, when it comes to the belief in the coming of Moshiach and the Resurrection of the Dead, we shy away from discussing it at all, as if we were ashamed to be connected with the subject! It is not relevant to our daily lives...Whoever is not totally involved in the complete belief of the Redemption and the Resurrection of the Dead is far from any true belief in G-d!
(Ohr Yechezkel, Rabbi Yechezkel Lowenstein, Ponoviz Yeshiva)
(L'Chaim)

Anyone who does not believe in Moshiach, or whoever does not look forward to his coming, denies not only the teachings of the other prophets but also those of the Torah and of Moses our teacher. (Maimonides' Mishne Torah, Laws of Kings 11:1)
(L'CHAIM)

We all believe with complete faith that tomorrow morning the sun will shine and bring light. One can wonder, How do we know this? Does the sun's shining today necessitate its shining tomorrow? Yes, for it is written so in the Torah: "Day and night shall not cease." Is there any greater faith than this? G-d declares in the Torah, "I swear that My glory will fill the entire world!" Our G-d guarantees that there will be a day when the glory of G-d will fill the entire universe...We should believe in the establishment of G-d's Kingdom in the entire world with the same certainty with which we await the daily rising of the sun. It is upon us to await and anticipate that great day. (Rabbi Chaim Yosef Dovid Azulay, the Chida)
(L'Chaim)

Our generation is the last generation of exile and the first generation of the Redemption. As my sainted father-in-law, the one whose yahrtzeit we commemorate, announced and publicized many times, all requirements have already been completed and all that is necessary is to actually greet our righteous Moshiach...Our Divine service consists of bringing the Redemption into reality, for this generation and for all generations preceding it! This means, that this generation concludes the work and Divine service of all preceding generations of Jews. (20 Shevat, 5752)
(L'Chaim)

Rabbi Abba said "There is no greater manifestation of the final redemption than this. As it is said: 'And you, mountains of Israel, you shall give forth your branches, and you shall bear your fruit for My people Israel, because they have come near' (Ezekiel 36). When the Land of Israel will give forth its fruit bountifully, then the Redemption will draw near, and there is no greater manifestation of the Redemption than this."
(L'Chaim)

Prior to the Redemption, when the quality of self-sacrifice for a higher goal is less understood, men dominate. Women, however, who represent a state of utter nullification to G-d will be truly appeciated in the Era of Moshiach. When G-dliness finally pervades the world openly, the uniqueness of her Divine essence will shine with remarkable radiance. (The Crown of Creation by Chana Weisberg)
(L'Chaim)

If the Jewish people begin now to rejoice already in the Redemption, out of absolute trust that G-d will speedily send us Moshiach, this joy in itself will (as it were) compel our Father in heaven to redeem them from exile. (Likutei Sichos, vol. 20 p. 384)(L'Chaim)

The Yalkut Shimoni states, "In the future, the Holy One, Blessed Be He, will sit... and expound a new Torah, which will be given by Moshiach." That is, there will be such a tremendous revelation of Torah wisdom that it will be considered a new Torah.
(L'Chaim)

The Talmud states that just as the dawn is the end of the night, so the Book of Esther was the end of the miracles that were given to be put in writing. It was the beginning of the dawn that would blaze to light with the coming of Moshiach, as it is written in Isaiah 60:1, "Arise, shine, for your light has come; G-d's glory shines upon you" (Me'am Loez)
(L'Chaim)

The coming of Moshiach has been likened to birth, for it is Moshiach who is alluded to in the verse in Psalms, "This day I have begotten you." Birth, in essence, is the revelation of an infant who had been concealed in its mother's womb. With the coming of Moshiach, the essential Four-Letter Name of G-d, which is now concealed in the Divine Name Elokim [connoting G-d's in this world within nature], will likewise become manifest. When a Jew stimulates the revelation of the Four-Letter Name by his fulfillment of the mitzvot, he brings nearer the self-revelation which will take place in time to come. (Torah Ohr)
(L'Chaim)

The distinctive goal and task of this generation is to bring Moshiach immediately. We want Moshiach now! There is nothing innovative about this. After all, every Jew requests in the prayers of Shemone Esrei [the Amida], "speedily cause the scion of David Your servant to flourish,... for we hope for Your salvation all day long." And when it is time for the afternoon prayers of Mincha, and Moshiach has not yet come, we say it again; and if (G-d forbid) the "speedily" is further delayed, we repeat the same prayer yet again in the evening prayers of Maariv! (Likutei Sichot of the Rebbe, vol 20)
(L'Chaim)

The word "redemption" applies only to one who emerges from darkness into light...We note in the long history of ours that troubles and dark sorrows become a basis for salvation and light; and the darker the troubles were, the greater was the light which came afterwards. The future redemption will also burst forth from the midst of darkness... And when will that moment be? In the month of Nisan, for G-d has appointed it as a time of redemption. (Book of Our Heritage)
(L'Chaim)

In the first few pages of the Hagada we read: "This year we are here; next year, may we be in the Land of Israel. This year, we are slaves; next year, may we be free people." On these words the Rebbe explains, "Mentioning the Land of Israel and our ultimate freedom at the beginning of the Hagada suggests that the purpose of the seder is not only to relive the exodus from Egypt, but to prepare for the Redemption."
(L'Chaim)

In order for there to have been the great revelation of the Torah at Mount Sinai there had to be an exile in Egypt of 210 years. Similarly, in order that there should be the great revelation of the inner teachings of the Torah in the ultimate Redemption, this exile has had to be so long. (Rabbi Shmuel of Lubavitch)
(L'Chaim)

" 'I shall return the captivity of My people Israel and they shall build the waste cities and settle... I shall plant them upon their land, and they shall no more be plucked out of their land that I have given them,' says G-d your G-d." (The Prophet Amos, 9:14-15)
(L'Chaim)

On Lag B'Omer, Rabbi Shimon Bar Yochai opened the pipeline of the inner meaning of the Torah, "Pnimiyut HaTorah." The study and dissemination of Pnimiyut HaTorah brings Moshiach. Rabbi Shimon told his son, "Until you see a keshet (rainbow)... do not expect to see the coming of Moshiach." This is why children play with a keshet v'chez (bows and and arrows) on Lag B'Omer, to show that Lag B'Omer is the appropriate time for the Redemption. (The Rebbe, Lag B'Omer, 1951)
(L'Chaim)

To ease the birth pangs of Moshiach, every individual should learn as much as possible. Each person is duty-bound to set aside time for daily study, which he should uphold unfailingly, never missing a day. (The Chofetz Chaim on Awaiting Moshiach)

Glory and might will be granted the righteous in the Time to Come. In what way? The Holy One, blessed is He, will sit in His house of study, and the eternally righteous will sit before Him, each radiating light according to the amount of Torah he possesses. (Tanna DeVei Eliyahu ch. 8)
(L'Chaim)

Shavuot is the anniversary of the passing of King David, the ancestor of Moshiach, as Maimonides' states in his Mishna Torah: If a king arises from the House of David who meditates on the Torah and occupies himself with the commandments like his ancestor David, in accordance with the written and oral Torah, and he will prevail upon all of Israel to walk in [the ways of the Torah] and strengthen its breaches, and he will fight the battles of G-d (defeating all the nations around him) - it may be assumed that he is Moshiach.
(L'Chaim)