The Messianic age represents the final fulfillment of G-d's purpose in creation. It is a time when evil will be vanquished, and good will reign over all mankind.(Waters of Eden, Rabbi Aryeh Kaplan)
(L'Chaim)

Our Sages have told us that the time before the coming of Moshiach will be a time of paradox. On the one hand, we will be able to perceive a glimmer of the future light, on the other hand, this era will be weighted down by a darkness so palpable that it will prevent the light from being properly perceived.(Overview to A Partner in the Dynamic of Creation by Malka Touger)
(L'Chaim)

The great Kabbalist and scholar Rabbi Levi Yitzchak Schneerson, father of the Lubavitcher Rebbe, passed away on the 20th of the Hebrew month of Av. His last audible words on the eve of his passing were, "Oh, the footsteps of Moshiach, the footsteps of Moshiach."(Y'Mei Chabad)
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Every adherent of the Law of Moses is obliged to believe in the coming of the Messiah. The Torah expressly commands us to believe the words of the prophet: "Unto him you shall hearken." But the prophets announced the coming of the Messiah, hence it is clear that one who does not believe in the coming of the Messiah denies the words of the prophets and transgresses a mandatory precept.(Albo, Ikkarim)
(L'Chaim)

The Midrash observes that when we respond "Amen" after the benedictions in the silent Amida concerning Resurrection, concerning the Final Redemption, and concerning the rebirth of Jerusalem (the 2nd, 7th and 14th) even though we have not yet witnessed these events and have not seen them occur, this is a sign of great faithfulness, concerning which the Prophet says, "The L-rd protects those who are faithful. (From Torah Faith: the Thirteen Principles by Rabbi Zecharia Fendel)
(L'Chaim)

From a letter of the Baal Shem Tov to his brother-in-law, Rabbi Gershon Kitov: "I ascended level after level, until I entered the chamber of Moshiach... I asked him, 'Master, when are you coming?' He replied, 'This is how you will know. When your teachings are known in the world and your wellsprings have spread to the outside...' "
(L'Chaim)

The Zohar states that the rainbow is one of the signs of the Redemption. The rainbow symbolizes the purification and refinement that the world underwent by means of the Flood. Before that time the clouds were made of coarser matter, which did not reflect sunlight. After the Flood had purified the world, the clouds too became more refined: they reflect sunlight, and a rainbow is produced. In this lies the connection between the rainbow and the Redemption, for at that time the entire physical world will attain the peak of refinement.(The Rebbe, Parshat Noach 5721-1960)
(L'Chaim)

Rav Saadia Gaon recounts as the ninth of his ten symbolic meanings in the sounding of the shofar on Rosh Hashana: To recall our faith in the future ingathering of Israel's dispersed, and to awaken our yearning for it. As it says in Isaiah (ch. 72): " And it shall be on that day - a great shofar will be sounded, and those who have perished in the land of Assyria, and those who were dispersed in the land of Egypt will come..."(The Book of Our Heritage)
(L'Chaim)

May it be Your will, L-rd our G-d and G-d of our fathers, merciful King, in Your abounding compassion, again to have mercy on us and on Your Sanctuary, and rebuild it soon and increase its glory. ...speedily reveal the glory of Your Kingship upon us; appear and be exalted over us before the eyes of all the living. Gather our dispersed from among the nations, and assemble our scattered from the ends of the earth. Bring us with song to Zion Your city, and with everlasting joy to Jerusalem Your Sanctuary
(From the Musaf prayer on Yom Kippur)
(L'Chaim)

"The voice of the herald brings good tidings and proclaims:...'The means and time of Redemption have been appointed; can a land be born in one day?...When the resplendent G-d redeems His people, then the evening shall be light... Turn to Me and be saved even this very day, if you heed My voice...Arise those who are buried in the earth; awake and jubilate, those who dwell in the dust...'" (From the prayers on Hoshana Rabba)
(L'Chaim)

Pondering that Moshiach and the Redemption are fundamental doctrines of the Divine Torah, studying and understanding the meaning of the laws and concepts of Moshiach, Redemption, the Messianic era and all that is related to these, must of itself evoke the appropriate appreciation and longing for these. (Mashiach by Rabbi J.I. Schochet)
(L'Chaim)

The final and concluding blessing of the Seven blessings recited at the wedding ceremony quotes a prophetic passage regarding the Era of Redemption - "...there shall speedily be heard in the cities of Judah and in the streets of Jerusalem, the sound of joy and the sound of happiness, the sound of a chassan and the sound of a kallah." This shall take place in the course of the true and complete Redemption, through Moshiach.(Hitvaaduyot 5745, Vol. V, pp. 2,883-4)
(L'Chaim)

The patriarchs exclaimed before Him: "Master of the universe, maybe there is no restoration for the children?" He said to them: "When there is a generation that looks forward to My Kingdom they will be redeemed immediately," as it is said (Jeremiah 31:16): "'There is hope for your future,' says G-d, 'that your children shall return to their own boundary.' " (Eicha Zuta 26)
(L'Chaim)

It is incumbent to await the coming of Moshiach every single day, and all day long... It is not enough to believe in the coming of Moshiach, but each day one must await his coming... Furthermore, it is not enough to await his coming every day, but it is to be in the manner of our prayer "We await Your salvation all the day," that is, to await and expect it every day, and all day long, literally every moment! (The Chafetz Chaim from Chizuk Emunah)
(L'Chaim)

The Torah hints at the great controversy of ikvesa dimeshicha (the time immediately preceding the coming of Moshiach), when all will say that they do not, Heaven forbid, doubt the possibility of Redemption; rather, they question its timing.(Chizuk HaEmunah, Chofetz Chaim Al HaTorah)
(L'Chaim)

Our Sages teach that when a person is judged after his death he is asked, "Did you look forward to salvation?" But where is the mitzva written?... Just as we are to believe that G-d brought us out of Egypt, as it is written, "I am the L-rd your G-d Who brought you out of the Land of Egypt,"... so too do I desire that you believe that I am the L-rd your G-d and that I am going to gather you in and save you."(The Semak, Positive Commandment 1)
(L'Chaim)

The reason this final exile of ours is lasting so long is because the light that will be revealed at the time of the Resurrection of the Dead and the World to Come is the greatest, most elevated light. (From the prayerbook with Chasidic commentaries of Rabbi Dov Ber, the "Mitteler Rebbe")
(L'Chaim)

"Before Rabbi Shneur Zalman was imprisoned in Petersburg, his Chasidic teachings 'burned the world'...no one who heard him delivering his Chasidic discourses remained the same as before. But after Rabbi Shneur Zalman's's release, his Chasidic teachings were more able to penetrate. And even more so after the release from his second imprisonment in Petersburg. The main goal was the revelation of the inner aspects of Torah; for in the times of Moshiach these inner teachings will be fully revealed. Thus, at the time of his release, a foretaste and sample of the Days of Moshiach was revealed. (Torat Shalom, page 26)
(L'Chaim)

The holy Rabbi Pinchas of Koritz, a leading disicple of the Baal Shem Tov, said: "Every Chanuka as the Chanuka lights are kindled, the hidden light is revealed-the light of our righteous Moshiach."
(L'Chaim)

The Chanuka menora has eight branches as compared to the menora in the Holy Temple which had only seven. Seven represents the natural cycle, i.e., the seven days of the week and the seven-year agricultural cycle, while eight symbolizes higher than nature-the supernatural level of Moshiach.
(L'Chaim)