The Biblical Messiah

Ani Ma'amin, I believe with a full heart in the coming of the Messiah, and even though he may tarry, I will wait for him on any day that he may come.
(One of Maimonides's Thirteen Principles of Faith - Telushkin, 1991, p. 545)
One of the continuing curiosities about Judaic messianism is its lack of solid, textual references. Franz Hesse says that the messianic idea is most evident in a variety of different passages when the Messiah is not mentioned. It is better to look for religious ideology and a future hope of redemption than to look for specific textual passages.
Critical View
The noun mashiah, messiah, annotatively means "anointed one." In Judaic texts, the term messiah was used for all kings, high priests, certain warriors, but never eschatological figures. In the Old Testament/Hebrew Bible, the term mashiah is used 38 times: two patriarchs, six high priests, once for Cyrus, 29 Israelite kings such as Saul and David. Not once is the word messiah used in reference to the awaited Messiah, the Son of God. Even in the apocalyptic book of Daniel, the only time mashiah is mentioned is in connection to a murdered high priest. The Dead Sea Scrolls, the Pseudepigrapha, and Apocrypha never mention the Messiah.
Lineage of the Messiah
The heritage of the awaited Messiah demonstrates that he could come from any race, ethnicity, and should be accepted without any discrimination. The Messiah is thought to be the descendant of King David. Unknown to many, King David's great-grandmother was a non-Jewish convert to Judaism. Ruth married Boaz and three generations later King David was born. The Messiah will be of the same line as both Ruth and David.
Coming of the Messiah
According to the Zohar, the major book of Kabbalism, the Messiah already exists in Paradise. It is not under any human control as to the time when the Messiah will come; God will bring the Messiah in His own time. When the time is right; when the time for judgment is upon us, the Messiah will descend upon the Earth. The Messiah will be ushered in by the aid of the prophet Elijah:
Behold, I will send you Elijah the prophet before the coming of the great and dreadful day of the Lord. (Malachi 4:5, King James Version)
Traditional Jewish thought is that the Messiah will present himself in Jerusalem by entering the Temple Mount via the Golden Gate, as prophesied in Ezekiel:
Then said the Lord unto me; This gate shall be shut, it shall not be opened, and no man shall enter in by it; because the Lord, the God of Israel, hath entered in by it, therefore it shall be shut. It is for the prince; the prince, he shall sit in it to eat bread before the Lord; he shall enter by the way of the porch of that gate, and shall go out by the way of the same. (Ezekiel 44:2-3, KJV)
Since God is the King, the prince referred to is the Messiah. The Messiah will then go to the site of the holy Temple; the House of God:
Behold, I will send my messenger, and he shall prepare the way before me: and the Lord, whom ye seek, shall suddenly come to his temple, even the messenger of the covenant, whom ye delight in: behold, he shall come, saith the Lord of hosts. (Malachi 3:1, KJV)
The Messiah paves the way for his Father, God, to come to Earth and make His judgments.
Judgment
God's judgment of all people will be based on the Commandments given to Moses:
Remember ye the law of Moses my servant, which I commanded unto him in Horeb for all Israel, with the statues and judgments. (Malachi 4:4)
God clearly specifies who He will judge and reject:
And I will come near to you to judgment; and I will be a swift witness against the sorcerers, and against the adulterers, and against false swearers, and against those that oppress the hireling in his wages, the widow, and the fatherless, and that turn aside the stranger from his right, and fear not me, saith the Lord of hosts. (Malachi 3:5)
The Old Testament texts and some of the non-universally accepted books such as Baruch, Sirach, and Apocrypha express God's commitment to the salvation of Jerusalem and the downfall of her enemies:
Then shall the offering of Judah and Jerusalem be pleasant unto the Lord, as in the days of old, and as in former years. (Malachi 3:4)
Take courage, O Jerusalem, for the one who named you will comfort you. Wretched will be those who mistreated you and who rejoiced at your fall. (Baruch 4:30-1)
Upon God's judgment of the people, He separates them into the redeemed and the fallen:
Then shall ye return, and discern between the righteous and the wicked, between him that serveth God and him that serveth him not. (Malachi 3:18)
During the time of Noah, in illo tempore, God was forced to bring about the Flood to wipe the Earth clean of heathens and sinners. At the time of the future redemption, the Earth will be cleansed by way of fire, a flood of fire:
For fire will come upon her from the Everlasting for many days, and for a long time she will be inhabited by demons. (Baruch 4:35)
For, behold, the day cometh, that shall burn as an oven; and all the proud, yea, and all that do wickedly, shall be stubble: and the day that cometh shall burn them up, saith the Lord of hosts, that it shall leave them neither root nor branch. But unto you that fear my name shall the Sun of righteousness arise with healing in his wings; and ye shall go forth, and grow up as calves of the stall. And ye shall tread down the wicked; for they shall be ashes under the soles of your feet in the day that I shall do this, saith the Lord of hosts. (Malachi 4:1-3)
The Sun of righteousness is a figurative reference to the Messiah. The book of Malachi ends the Old Testament and leaves Jewish believers with the expectation of Elijah ushering in the coming Messiah. Thus Jews have anticipated their redeemer to come and save them and cause the destruction of their enemies.
Era of Peace
The Messiah's appearance on Earth will usher in the messianic age; an era of peace. This period will be characterized by peace and justice for all the righteous. Believers will flock to the holy city of Jerusalem where God will give them His knowledge:
And it shall come to pass in the last days, that the mountain of the Lord's house shall be established in the top of the mountains, and shall be exalted above the hills; and all nations shall flow unto it. (Isaiah 2:2, KJV)
The setting of this scene is the messianic age and the mountain described is holy Jerusalem where the Temple, God's house, is located. The righteous nations will go toward the axis mundi to be as close to God as possible. And He shall present them with wisdom:
And many people shall go and say, Come ye, and let us go up to the mountain of the Lord, to the house of the God of Jacob; and he will teach us of his ways, and we will walk in his paths: for out of Zion shall go forth the law, and the word of the Lord from Jerusalem. (Isaiah 2:3, KJV)
Part of His wisdom will be the importance of judgment of all nations and peace between all people:
And he shall judge among the nations, and shall rebuke many people: and they shall beat their swords into plowshares, and their spears into pruninghooks: nation shall not lift up sword against nation, neither shall they learn war any more. (Isaiah 2:4, KJV)
War will no longer exist among the nations; enemies will be allies in the messianic age. This sentiment is present in other texts as well:
The wolf also shall dwell with the lamb, and the leopard shall lie down with the kid; and the calf and the young lion and the fatling together; and a little child shall lead them...They shall not hurt nor destroy in all my holy mountain: for the earth shall be full of the knowledge of the Lord, as the waters cover the sea. (Isaiah 11:6,9, KJV)
Notice the use of vicious animals such as the wolf, leopard, and lion to portray the Jews' enemies. The Jews themselves are characterized as the lamb and calf; helpless, innocent animals. The messianic age will be full of peace and goodwill, even down to the animal world. And the world will known the knowledge of the Lord. The kingdom that God and the Messiah set up will be the most powerful kingdom and it will be indestructible:
And in the days of these kings shall the God of heaven set up a kingdom, which shall never be destroyed: and the kingdom shall not be left to other people, but it shall break in pieces and consume all these kingdoms, and it shall stand for ever. (Daniel 2:44, KJV)
Some believers say that the city of Jerusalem and the holy Temple will be indestructible when the Messiah comes, possibly by being made out of laser beams or energy (see Jerusalem). The emphasis in Judaism is on the notion of peace and justice between the nations and the reason that Jews don't believe Jesus was the Messiah is that they don't believe He brought about such changes (see Jesus vs Jewish Messiah).
Just to repeat, concerning Biblical texts and the notion of th Jewish Messiah, it is necessary to look at scriptures that may not mention the Messiah, mishiah, but that have future connotations of hope, salvation, and peace.