To unlock this area, you need to complete the "Restoration" mission. The bridge built thanks to your help will lead you to Driftwood.
" Dangerous Things: Stargazing in Remote Areas"
After completing "Restoration" and " Gift Wood for Driftwood", head onto the largest island on the left . You will find a mine entrance right beside the path .
Go inside and take a good look around . The book will be lying on the nearby crates .