Don't know what to look for? Here are a few great books we recommend:

Paul Magriel Backgammon
Danny Kleinman Vision Laughs at Counting (two volumes)
Bill Robertie Advanced Backgammon (2nd edition, two volumes)
Kit Woolsey Tournament Series Backgammon
Kit Woolsey and Hal Heinrich New Ideas in Backgammon

Out-of-print books are available from libraries, used book stores, internet auction sites, and collectors.