John Marenbon is a good go-to. He has edited two books which should be your start. His Boethius (Oxford, 2003) is a thorough overview. But even better is the volume he edited Companion to Boethius (Cambridge, 2009), which collects numerous different essays/chapters pertaining to Boetheius and his milieu from various scholars. On topics for which they exist, the Cambridge Companion books are generally excellent for an easy entry to that topic.

There is also Margaret Gibson's Boethius, His Life, Thought, and Influence (Oxford: Blackwell, 1981). It is pretty old now but is probably still perfectly fine as an intro.