Books on the accountability, the coaching stance behind it, and the organisational work that takes up most of the role.
Most of the Scrum Master job is not running events. It is coaching, facilitation and changing the conditions around a team, and the books that help are not all Scrum books. This list starts with the framework, moves to the coaching craft, and finishes with the organisational material you need once the team itself is working well.
The accurate short reference on the framework. Read it first so that everything else is measured against what Scrum actually says.
The standard book on the coaching side of the role, covering the shift from expert to coach and the stances the job moves between.
The State of Mind model and the levels of system the role works across, from the team out to the whole organisation. Practical about daily activity.
Paired examples of the ordinary approach next to the stronger one, which makes the difference between competent and good concrete.
A five stage structure and a catalogue of activities with timings. The book that stops retrospectives becoming the same conversation every fortnight.
The comprehensive reference for the questions that come up when someone challenges a practice and you need the reasoning behind it.
The Scrum Master role is largely difficult conversations. This gives you a repeatable structure for the ones where the stakes are high.
For when the impediment is the shape of the organisation rather than anything inside the team.
Cohn on adoption beyond a single team, including the patterns for spreading practice and the resistance you will meet.
Flow metrics give you something to say about predictability that does not depend on velocity, which is where most Scrum Master credibility is won or lost.
Sutherland on where Scrum came from and the reasoning behind it. Useful when you need to explain to someone outside the team why short iterations and cross functional teams work, rather than what the events are.