
A lot of folks here will have read either Rosencrantz & Guildenstern Are Dead or Arcadia, which are still probably his best plays, and certainly the best introduction to his work. I personally also really like The Invention of Love, about the gloomy tortured homosexual poet and classical scholar A.E. Housman, which was also apparently Stoppard's favorite of his plays. It's definitely niche territory though and you might need to care at least just a little about A Shropshire Lad and latin textual criticism. The Coast of Utopia is even more packed with history and erudition, although worth a read; the currently top comment here is a quote from it about death, childhood, and the pursuit of happiness.
He had an interesting combination of traits that many HN readers will probably appreciate: erudite to the point of elitism, although never attended college; a self-described "small c. conservative in politics, literature, education and theatre" with libertarian inclinations, but he wrote a sprawling trilogy about 19th-century Russian socialist and anarchist exiles (The Coast of Utopia).
Now that he's dead, I want to go back and re-read all his plays, including the ones I never managed to get to before.
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