Well, the classic history is Frederic C. Lane, Venice: A Maritime Republic (Johns Hopkins University Press, 1973), but it's actually very long and it's not really something anyone could read in a week...

A more recent and much more readable book is Thomas Madden, Venice: A New History (Penguin, 2012).

Otherwise I don't think there really are any simple books about the entire history of the republic. There are lots of books about specific periods/topics, but for a general history you'd have to use either Lane or Madden.

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