Rabbi Jacob Immanuel Schochet’s work Mashiach: The Principle of Mashiach and the Messianic Era in Jewish Law and Tradition, is perhaps the best on the topic in English if you cannot access Hebrew or Arabic to read the source texts. This is one of the most important texts to read on the topic. Some people have been fed lies or camp fire stories on the topic of the Messiah (Heb. Mashiach and Ar. Masih) and this has then shaped their thinking when discussing with Jewish people regarding Islam.
The topic of the Messiah in Judaism is well defined and the agreed upon texts are those codified by the Rabbi, Moshe Ben Maimon (AD 1135-1204), famously known as Maimonides or shortened to RAMBAM. His systematic theology and unequivocal declaration on the Messiah is clear: “I believe with complete faith in the coming of Mashiach. Though he tarry, nonetheless I await him every day that he will come.” Principles of Faith, no. 12.
Maimonides, no doubt looking around and borrowing the theological premises and technical language of Muslim theologians in Egypt, Iberia, Morocco and transferring it to Judaism (his books being written in Arabic), came to be the gold standard for defining Jewish doctrine. The believe in the Messiah is the 12th of the thirteen main principles of Jewish theology and one cannot be considered Jewish without these principles firmly believed. Please see Louis Jacobs’ Concise Companion to the Jewish Religion, pp. 183-184, Oxford University Press, 1999, London.
Schochet, an accomplished theologian, lays out the understanding that the Messiah is actually two: the forerunner, referred to as Mashiach Ben Yossef and the actual Mashiach, son of Dawood. The first Mashiach is the forerunner, announcing the coming of the true Messiah. He will let the world know of his coming. When the Messiah does arrive, Mashiach Ben Yossef will act as his viceroy. In addition to this, the Prophet Eliyahu (Eng. Elijah) will return before the Messiah and proclaim truths.
The Prophet Eliyahu will cause the Children of Israel to repent, to be involved with the resurrection of some of the dead, to restore some of the relics that will later be installed in the Third Temple and also announce the Messiah.
Upon the coming of the Messiah, Mashiach Ben Dawood, he will build the Third Temple and restore the Jewish people. In fact, it is categorically maintained by Rabbinical Judaism in pp. 73-74:
“The Messianic King will arise in the future and restore the Davidic Kingdom to its’ former state and original sovereignty. He will build the Sanctuary and gather the dispersed of Israel. All the laws will be re-instituted in his days as they had been aforetimes; sacrifices will be offered, and the Sabbatical years and Jubilee years will be observed fully as ordained by the Torah. Anyone who does not believe in [Mashiach], 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.”
The Messiah is also supposed to bring in the following affairs in his era: Restoration of the Temple, Gathering of the Exiles back to the land of Israel, End to Evil and Sin, Awareness and Knowledge of God, Universal Worship of God, Universal Peace and Harmony, Resurrection of the Dead and Blissful Utopia: End to Disease and Death, Mashiach, pp. 19-33.
This is a well researched text and also eye opening for the one who wants to understand this issue. The reader should keep in mind that these formulations of Maimonides have come thousands of years after the first century, thus one is able to see that it is coloured with a dislike of the claim that Muslims have that the Prophet `Isa ibn Maryam, peace be upon him, is the Messiah and shall come again to rule.
Overall, Schochet’s work is a masterpiece and has exquisite comparative value in regard to the topic of the Messiah. If someone wants to understand the 1,000 years+ of Rabbinic Judaism and its’ development, then this book is the right one for you. Outside of the Qur’an and Sunnah, this is a short but detailed 101 page slim manual.