There are many sources from Tanach, Midrash, and Gemara. The Amidah prayer that a Jew says 3 times a day written by the men of the great assembly (era ending 70C.E. aprox.) speaks of Moshiach in blessing 15. Request for Moshiach (scion of David) and salvation.
In the beginning G-d created the heavens and the earth... and the spirit of G-d hovered over the waters...
("The spirit of G-d hovered" -- this is the spirit of Moshiach - Midrash Rabbah).
It shall come to pass in the last days, that the mount of the house of G-d shall be established atop the mountains, and be exalted above the hills; and all nations shall stream to it.
And many nations will go, and say: "Come, let us go up to the mountain of G-d, to the house of the G-d of Jacob; and he (Moshiach) will teach us of His ways and we will walk in His paths." For from Zion shall go forth Torah, and the word of G-d from Jerusalem.
And he (Moshiach) will judge between nations, and decide among the peoples.
And they shall beat their swords into plowshares, and their spears into pruning hooks. Nation shall not lift up sword upon nation, neither shall they learn war any more.
On the day that the Holy Temple was destroyed, a Jew was plowing his field when his cow suddenly called out. An Arab was passing by and heard the call of the cow. Said the Arab to the Jew: "Son of Judah! Unyoke your cow, free the stake of your plow, for your Holy Temple has now been destroyed." The cow then called a second time. Said the Arab to the Jew: "Son of Judah! Yoke your cow, reset the stake of your plow, for Moshiach has now been born."
Said Rabbi Bon: "Do we need to learn this from an Arab? The Torah itself says so. The verse predicts "The great tree shall be felled by the mighty one." And what is written immediately following? "There shall come forth a shoot out of the stem of Yishai..."
Source - Jerusalem Talmud, Brachot 2:4
In the future era of Moshiach G-d will slaughter the inclination for evil.
-Talmud, Sukah 52a
All deadlines for the coming of Moshiach have come and gone - the thing depends solely on our returning to G-d.
-Talmud, Sanhedrin 97b