I've posted a top level comment as I felt it was worth it, but the last surviving prosecutor passed away April 2023 and wrote multiple inspiring works on the topic. Lookup Ben Ferencz' 'Parting Words' . While the book doesn't spend its entire time on the trial, it discusses the difficulties of holding people accountable for war crimes (even today).

The movie "Judgment at Nuremberg" (1961) is the classic summary. It's a docu-drama, but reasonably accurate. All the big stars of the day, from Spencer Tracy to Judy Garland. William Shatner has a minor role.

I'd be very curious to see what people recommend since I think it's very important to consider how the victors behaved at the end of the war. I studied some details about Nuremberg while in law school, from an Anglo American legal point of view, and then I spent a lot of time on wikipedia learning the historical background of the individuals involved.

The Final Reckoning: Nuremburg Diaries by Boris Polevoi provides a Soviet perspective.

Also it is full of courtroom art/sketches from the proceedings.

Eichmann in My Hands by Peter Malkin