Felix is the artistic director for a Canadian theatre where he presents avant-garde productions of Shakespeare plays. Right away he's ousted by his second in command, Tony. Felix becomes something of a hermit and removes himself from society for a while, until he starts teaching Shakespeare to some prisoners at a local jail, under the name Mr Duke. Sound familiar? If it doesn't, you probably need to brush up on The Tempest. I'm curious whether those who are not well-versed in the play would enjoy the book as much as one who isn't but my guess would be no. Following the connections in part of the fun; wondering how she's possibly going to wrap it up, knowing the original ending, is like watching the master at work. Anyway, it's a problem easily remedied, so, if you haven't read The Tempest before, give it a quick read before Hag-Seed and I think you'll find your experience improved.
Although Felix thinks things like "If anyone had told him then that he'd be doing Shakespeare with a pack of cons inside the slammer he'd have said they were hallucinating" he's actually a very good teacher with excellent critical thinking assignments for his players and a respectful attitude toward their strengths, with very little interest in their criminal backgrounds.
Shakespeare was famous for putting a "play within the play" and Atwood took that concept to the extreme. At one point I think I counted five plays within the play but I did allow myself to get pretty meta - are we not all players upon the stage, etc.? Hag-Seed is a joy to read and Atwood's joy in writing it is evident as well - she clearly knows the theatre very well.
Crises of confidence have been surmounted, grudges incurred, hurt feelings soothed. Felix has berated himself for his own lunacy in undertaking such a hopeless enterprise, then congratulated himself on his judgment. His spirits plunge, then soar, then plunge again.