What is the best-known book set in Estonia?

See note on methodology

Finishing off the former Soviet republics, there’s a runaway winner here, most owned and most often tagged Estonia on both LibraryThing and Goodreads. Its author is Estonian by origin, but writes in Finnish; the novel of 2008 is based on a play first performed in 2007 about sexual violence in the Soviet occupation of Estonia, and the present day. It is:

Purge / Puhdistus, by Sofi Oksanen

She also takes second place on Goodreads with a 2003 novel about eating disorders and teh historical relationships between Finland, Estonia and Russia:

Stalinin lehmät / Stalin’s Cows, by Sofi Oksanen

Third on GR is a 1981 collection of autobiographical short stories by a Russian journalist who worked in Soviet Estonia during the early 1970s (apparently very funny): 

The Compromise / Компромисс, by Sergei Dovlatov

Second and third place on LT go to representatives of a particular non-fiction tradition that is well-represented there, the first published in 2000, the second in 2008:

Knitted Lace of Estonia: Techniques, Patterns, and Traditions, by Nancy Bush
Folk Knitting in Estonia : A Garland of Symbolism, Tradition, and Technique, by Nancy Bush

Other Estonian writers to note: Oskar Luts, A.H. Tammsaare, August Kitzberg, Jaan Kross, Margus Karu.