The Singing Revolution by various — not a single book but a concept worth reading about before you visit. The documentary of the same name is excellent. Estonians resisted Soviet occupation through choral singing, maintaining national identity through song festivals that the Soviets couldn't easily ban. The final mass singing demonstrations in 1987–1991 helped precipitate independence.
The Czar's Madman by Jaan Kross (1978, translated) — Estonia's most celebrated novelist. Set in the early 19th century under Russian rule, this is a novel about an Estonian nobleman who marries a serf woman and writes a letter criticising the Tsar, then feigns madness to survive. Beautifully written and an excellent introduction to Estonia's relationship with its successive occupiers.
The Nightwatchers by Boris Akunin — a thriller set partly in old Tallinn, written by the Georgian-Russian mystery novelist. Not deep but good company on a train or ferry.
The Baltic States: Estonia, Latvia and Lithuania by David J. Smith (2002) — the clearest short academic history of the region covering the independence periods, Soviet occupation, and post-Soviet transition. Useful context for everything you'll see.