This short post over at the Exegetical Tools blog draws attention to accessible introductions to the Septuagint. Several books on the Septuagint are mentioned:
Invitation to the Septuagint, by Jobes and Silva
The Septuagint (Understanding the Bible and Its World), by Dines
The Use of the Septuagint in New Testament Research, by McLay
Of those three, Jobes and Silva is recommended as an introduction. It’s quite readable.