The following is excerpted from Hans Lietzmann’s monumental four volume work:
 A History of the Early Church, Vol. I, The Beginnings of the Christian Church, (Translated by Bertram Lee Woolf), pg. 87-91, The World Publishing Company, New York, 1967

   "In spite of all the close connections maintained with Jerusalem and all the common feeling, the Judaism of the Diaspora had, in the course of time, come to differ in character from that of the people of the native land. The most striking instance was the fact that they had forgotten the language of Palestine, and accepted the Greek of everyday use. The change was due to the history of the Jewish people, who had long abandoned their mother-tongue even in Palestine. When the exiles returned from Babylon, they brought with them the current Aramaic language, and retained it for a millennium. Hebrew remained the sacred language of scholars for religious usage, and the discussions in the Mishna were written down in Hebrew even in the second century A.D. But the Talmuds of the fourth and fifth centuries, being in Aramaic, show that Hebrew was obsolete even in the theological schools.

"Valuable documents of the fifth century B.C. belonging to the Egyptian Diaspora and written in Aramaic have been found in Elephantine. An interpolation in the text of Isaiah (19: 18) mentions five Egyptian towns in which “the language of Canaan” was spoken.
"In the Ptolemaic period we still find traces of Aramaic in upper Egypt and in Alexandria; but about this time, Greek began to be used by Jews, both as the language of the administration, and in everyday life. In the latest period of the Ptolemies, the Jews of Onias not only wrote Greek epitaphs for their dead, but also bewailed the loss of the departed in elegiac poems formed on Hellenistic models and mentioning Hades as well as Moira. In the entire remainder of the Mediterranean world, the memorial tablets of the Jewish Diaspora are almost exclusively in Greek. Here and there is a Hebrew phrase, e.g. shalom=peace, or shalom al Israel=peace be to Israel, upon a gravestone, but inscriptions genuinely composed in Hebrew or Aramaic are very rare. The common opinion that the adjective, “Hebrew”, points to communities speaking Hebrew or Aramaic, is mistaken. The door-post of a synagogue has been found at Corinth’ bearing the name of the congregation: “Synagogue of the Hebrews.” But these Hebrews did not speak Hebrew, for the inscription is in Greek! Outside Palestine, only the Rabbis knew any Hebrew - but no one knows how many they were, nor how much they knew. The remote region of the Crimea is alone in preserving Hebrew inscriptions of the first to the fourth century A.D.

"This change of language, both at home and in the Diaspora, was not without far-reaching effects upon public worship. The ancient custom of reading the Hebrew  scriptures in the synagogue necessitated a translation into the Aramaic which the people understood, the original text and the translation followed one another verse for verse. Dubious passages were not translated, but read only in Hebrew. Originally the translations were extemporaneous, but naturally they soon assumed forms fixed by tradition. Out of these forms grew the Aramaic Targums, which were at last put into writing in the Talmudic era, i.e. about the fifth century. Moreover the liturgical prayers, which Jewish prayer books even to-day preserve in their original Hebrew form, were said by the people in the vernacular. The Mishna expressly permitted it, and a shrewd Rabbi rightly told an objector that it was better to do so than that the people should not pray at a1l.  Nevertheless, this reply seems rather to evade the real point, and Charlemagne gave a better reason for using German in the Lord’s Prayer.

"An Aramaic targum was current in Palestine, side by side with the original Hebrew, and a Greek translation in the Diaspora for public worship in the synagogue. Known and preserved as the Septuagint, or LXX, the latter originated in Alexandria. The first part to be translated was the most important, and it took premier place also in public worship. This was the Pentateuch, the Greek version of which was current as early as the end of the third century B.C. The prophets and the other books followed gradually and by various translators. Soon after 116 B.C., a grandson of Jesus Sirach was familiar with the whole of the Old Testament in Greek. At the time of the early Roman empire, as is shown by the use made of it by Philo and Paul, the LXX was the universally recognized Bible of the Diaspora, even for the purposes of divine worship.

"In Alexandria, an annual festival was held on the Pharos island, when the people gave thanks for this translation. There seem to have been several translations of isolated books current at the same time, but they disappeared early almost without trace. It was the rivalry of the Christian Church which had made the LXX equally its own, that gave rise, after the second century, to newer and more literal translations for Jewish use. In the nature of the case, it is doubtful whether the original Hebrew was read alongside the translation; possibly custom varied. By the time of the emperor Justinian, greater emphasis was placed on the reading of the original in public worship, and the question was discussed whether any translation at all could be read aloud along with it. These facts show that the influence of the Judaism of the Talmud had grown, but do not prove what was the custom elsewhere in the Empire centuries earlier.

"Not only were the Scriptures read in Greek, but also the same language was used for the prayers and the confession of faith, i.e. the “Shema,” in the public worship of the synagogue. The sources testify to this fact in regard to Caesarea, the quasi-gentile capital of Palestine, and naturally the same holds good for the Diaspora in general. Only just recently have scholars traced out a little Greek prayer-book of the Jewish synagogues that dates from the second century A.D., and that is enshrined in a Christian liturgy of the fourth century. This discovery is very suggestive. It is only a drop out of the ocean, but it makes quite clear how little is really known about worship in the synagogues of the Greek Diaspora. We may take it for granted that this worship, not only changed in the course of centuries, but also differed in different places; and moreover that there were many different degrees of Hellenization.

"Besides reading and prayer there were exegesis and preaching, of course in Greek. The collective term, deuterosis, was given to the traditional elements here. The term is a liberal translation of the Hebrew Mishna, i.e. repetition, and it included everything deduced from, or built on the Law or the historical records of the sacred text: hence the Halakha or specialized legal casuistic, and the Haggada, the Biblical legends. Even Augustine testified that this deuterosis was passed on only by word of mouth, not written down - showing that the Diaspora followed the example of Palestine. It follows that there was a Greek Halakha and a Greek Haggada; or, to put it otherwise, the Diaspora possessed a Greek Midrash and a Greek Talmud. Traces of both often occur in Paul, Philo, Josephus, and the Apocrypha—but no actual documents, and it is scarcely probable that much was written down. Indeed, everything of this kind disappeared when the Judaism of the Greek Diaspora ceased to be.

"Very little evidence has survived affording a true idea of the cultural life of the Hellenistic Diaspora. Most information refers to Egypt. The LXX translation was made here, and it was here that Pseudo-Aristeas was at home. III Maccabees, perhaps IV Maccabees, and the Wisdom of Solomon were written in Egypt, and here Philo labored. Other regions afford little information about Judaism, whereas, in regard to the contemporary beginnings of Christianity, it is precisely Egypt that is quite blank. Nevertheless Alexandria distributed its Greek Bible throughout the whole of Judaism, and, except Jerusalem, was apparently the only spiritually productive centre of Israel. This fact makes it possible, within bounds, to generalize the phenomena obtaining there."