On the Web
This listing from the Central Europe Review is a good starting point for doing research on Tarkovsky.
List of books on Central and European Cinema recommended by Central Europe Review Excellent bibliography that includes books on Russian cinema, as well as Eisenstein, Tarkovsky, and Kieslowski.
Taylor, Richard, ed., et al. The BFI Companion to Eastern European and Russian Film. London: BFI Publishing, 2000. A dictionary-like reference film--not very deep but useful.
Gillespie, David. Russian Cinema. England: Pearson Educational Limited, 2003. Good historic overview, from Eisenstein to Tarkovsky.
Goulding, Daniel J. Five Filmmakers. Bloomington: Indiana University Press, 1994. Excellent sections on Tarkovsky, Forman, Polanski, Szabo and Makavejev.