Could also be a really really good book on Russians.
But the classic Russian writers are famous because of their writing, same as French, English and American authors are.
Some of the most famous Russian books include 'Anna Karenina', 'War and Peace' and 'Doctor Zhivago', and these three have been made into Russian and/or Western films. Like all films, the film versions often cut out whole swathes of the original story, but can give an outline of what the books contain.
Dostoevsky has some exciting and thought provoking books (if you put aside his antisemitism and religious fanatism).
Pushkin has some great prose and poetry.
Some people find Nabokov a great writer.
Pelevin - is the only modern Russian writer worth reading and enjoying. His fiction among other themes is also a great and precise satirical reflection of a modern Russian society.
I've been meaning to get to Victor Pelevin's The Life of Insects for a while.
From my memory,
a) Brothers Karamazov (Dosteovsky)
b) Crime and Punishment (Dosteovsky)
c) Master and Margarita (Bulgakov)
d) Short stories of Checkhov
e) Pale fire (Nabakov).
Not sure if you would consider Nabakov as Russian or American, but his prose has clarity and is hypnotic.
Look up writers and playwrights associated with the Nihilist Movement if you want the explosive stuff (the writings that would ignite the Revolution many years later), although I can't personally speak for the quality of such works outside the authors I've mentioned.
While she didn't write for a Russian audience despite being of Russian descent herself, Ayn Rand's novels certainly have the literary approach of the 19th century Russian novel and the style of 20th century film noir.
If you want early science fiction, there's Aelita by Aleksy Tolstoy and We by Yevgeny Zamyatin (with the latter considered the grand-daddy of dystopian fiction as we know it)