The Babylonians ruled the world in the sixth century B.C. Yet, afterwards, in the course of about half a century, they ceased to exist. This is remarkable enough, but it is even more astounding that their successors, the Persians, had did not existed before! In 560 B.C., Cyrus the Great became the king of Persia, a small state in the Middle East, and within 30 years had replaced the Babylonian empire with his own.
Cyrus also unexpectedly told the Jews that they could return to their homeland. While he was probably motivated primarily by the desire to have someone else rebuild Palestine and to make it a source of income for the Persian Empire, the impact on the Jews was to reinvigorate their faith and stimulate them to reconstruct the Temple in Jerusalem. The Second Temple was completed on the very site of the first Temple in 516 B.C.
Though Cyrus allowed the Jews freedom to practice their religion, he would not permit them to reestablish the monarchy. Instead, Cyrus sent Zerubbabel, a prince of the house of David, along with 42,360 other exiles to establish what essentially became a theocracy, with Zerubbabel as High Priest.
Over the next 150 years, Judea flourished as the Jews rebuilt Jerusalem and developed the surrounding areas. The Persians resisted any Jewish efforts to restore the monarchy, but allowed them a high degree of autonomy under the High Priest, whose power was partially checked by the Sanhedrin, the Jewish Court, and the Popular Assemblies.
During this period, Judaism's Written Law took its final form. One of the key changes in the history of Judaism was the imposition at this time of a ban on intermarriage between Jews and non-Jews. Though from that point to the present, the adherence to this rule has not been universal, it is one of the central tenets of Judaism and perhaps the most important reason for the survival of the Jewish people., Unlike other peoples, they did not disappear through assimilation and intermarriage.
Sources: Mitchell G. Bard, The Complete Idiot's Guide to Middle East Conflict. 4th Edition. NY: Alpha Books, 2008.