Bibliotheca Alexandrina

Alexandria was home to the largest community of Jews outside of Palestine, and many of them no longer spoke Hebrew (Paleo-Hebrew or Pre-Persian Hebrew) but rather Koine Greek, the lingua franca of the Mediterranean kingdoms.

According to tradition, the translation was also found at the famous Library of Alexandria, which was part of a religious institution and home to valuable texts for Christianity and Judaism and other religions from preceding eras.

The name "Septuagint" (Latin for "seventy") comes from the legend in the Letter of Aristeas that 72 Jewish elders were each placed in a separate room and miraculously produced identical translations of the Torah. However extant copies of the Septuagint have variants. As do all extant copies of any text type.

There is no single book (like the Samaritan Pentateuch Abisha Scroll) which represents LXX, however there are various fragments throughout Africa and Asia and Europe. A close example extant today is Cave 4 and 7 of the Qumran caves by Palestine.
https://hermeneutics.stackexchange.com/questions/21872/what-are-the-oldest-copies-we-have-of-lxx. For modern english LXX translations consider:

Lexham English Septuagint (for reading) and personal use.

NETS (A New English Translation of the Septuagint) which is good for study and includes various LXX variations.

Or Brenton (free online); but this one attempts to match the structure of the LV.