And it so chanced that the work of translation was completed in seventy-two days, just as if this had been arranged of set purpose. - The Letter of Aristeas
AKA the Greek Old Testament, the Translation of the Seventy, LXX
(255 A.D.)
The Bible of choice at the time of Christ by Christians.
The Septuagint is the only Hebrew-to-Greek translation of the Hebrew Bible that survived fully intact. Other Greek versions included Aquila's A.D. 130 clunky literal translation used by Jews, Symmachus's A.D. 170 accurate but readable translation, and Theodocian's late 2nd century A.D. apparent revision of an earlier Greek version.
(https://overviewbible.com/septuagint/, Origin of the Bible handout by my small group leader, February 8, 2023. Summarized from Wikipedia. Page 3; The Origin of the Bible: Newly Updated by F. F. Bruce, J. I. Packer, Philip W. Comfort, and Carl F. H. Henry, 2020. Texts and Manuscripts of the Old Testament by Mark R. Norton, Page 169-170)
Differences between the Masoretic texts
It is older than the Masoretic texts, and there are differences between them. There are arguments whether Jesus used the Septuagint or another Bible, and arguments whether the Septuagint or the Masoretic texts are more accurate.
(Origin of the Bible handout by my small group leader, March 22, 2023. Page 2.)
Since the Septuagint includes Apocrypha, the Alexandrian canon of Jews living in Alexandria is theorized to be broader than the Palestinian canon of Jews living in Palestine. The Alexandrian canon matches the Palestinian canon, shown by Philo of Alexandria's writings. The divisions are the same, and inspiration is only attributed to the canonical books, not the Apocrypha.
In the Septuagint manuscripts, the Prophets and Hagiographa have been rearranged by Christian hands in a non-Jewish manner and intermingled with the Apocrypha.
(The Origin of the Bible: Newly Updated by F. F. Bruce, J. I. Packer, Philip W. Comfort, and Carl F. H. Henry, 2020. The Canon of the Old Testament by R. T. Beckwith. Pages 62.)
History
The Letter of Aristeas describes the Septuagint's development. (https://www.ccel.org/c/charles/otpseudepig/aristeas.htm)
Ptolemy II hired 72 Jewish scholars who in 72 days translated the entire Old Testament into Greek, the language used by the Jewish community in Egypt. There were many translations for the Greek, but this legend underlines the sole Greek authorization of the Septuagint.
The date of translation is unknown, but the Pentateuch was completed in the 3rd century B.C., with the rest completed over a long period of time by many different scholars.
(Hillsdale College - Ancient Christianity, The Origin of the Bible: Newly Updated by F. F. Bruce, J. I. Packer, Philip W. Comfort, and Carl F. H. Henry, 2020. Texts and Manuscripts of the Old Testament by Mark R. Norton, Page 168)
Translation
The translations of the individual books are not uniform. Many books are translated almost literally, while Job and Daniel are more dynamic.
(The Origin of the Bible: Newly Updated by F. F. Bruce, J. I. Packer, Philip W. Comfort, and Carl F. H. Henry, 2020. Texts and Manuscripts of the Old Testament by Mark R. Norton, Page 168)
Textual Criticism
The more literal books are more valuable to examine than the dynamic ones. Jeremiah is missing significant portions found in the Masoretic Text, and the order of the text is significantly different as well. It's unknown if this is due to a poor translation that misses portions of the original Hebrew or to editorial additions and changes in the Masoretic texts. Maybe there were a number of valid textual traditions at that time, and the Septuagint and Masoretic Text followed different ones.
(The Origin of the Bible: Newly Updated by F. F. Bruce, J. I. Packer, Philip W. Comfort, and Carl F. H. Henry, 2020. Texts and Manuscripts of the Old Testament by Mark R. Norton, Page 168-169)
Which Bible did Jesus read?
The New Testament writers quote the Septuagint, Targums, or an ad hoc rendering of the Hebrew. By the time of Christ, the majority of people, even Jews, spoke Aramaic and Greek, not Hebrew.
(The Origin of the Bible: Newly Updated by F. F. Bruce, J. I. Packer, Philip W. Comfort, and Carl F. H. Henry, 2020. Biblical Languages by Larry Walker. Section One: The Authority and Inspiration of the Bible. Page 35; The Origin of the Bible: Newly Updated by F. F. Bruce, J. I. Packer, Philip W. Comfort, and Carl F. H. Henry, 2020. Texts and Manuscripts of the Old Testament by Mark R. Norton, Page 169)
The early Church Fathers outside of Palestine and Syria normally used the Septuagint or the derived Old Latin version.
(The Origin of the Bible: Newly Updated by F. F. Bruce, J. I. Packer, Philip W. Comfort, and Carl F. H. Henry, 2020. The Canon of the Old Testament by R. T. Beckwith. Pages 63.)
List of Books
Books are arranged in similarity of subject matter. Via the Vulgate, most Christian editions follow this order.
(The Origin of the Bible: Newly Updated by F. F. Bruce, J. I. Packer, Philip W. Comfort, and Carl F. H. Henry, 2020. Section One: The Authority and Inspiration of the Bible. Page 6.)
The exact list of books differs depending on the manuscript. Some major ones include the Codex Vaticanus, the Codex Sinaiticus, and the Codex Alexandrinus.