I'm looking for a general overview history of the Republic of Venice, or (if a one-volume history of the whole period is too much to ask) at least something that covers the republic's height. I'm mainly interested in political/institutional history, the way that governance worked and so on, but more culture-focused approaches are not unwelcome.
Roger Crowley's City of Fortune: How Venice Won and Lost a Naval Empire is a really good overview. It covers the political, military, and technological history of Venice in a really informative and engaging way.
Venice: A New History by Thomas F Madden is a really good overview of the history of Venice. It was written relatively recently and was intended to be accessible to a less academic focused audience.
Personally, I really enjoyed the book and can't recommend it enough to anyone looking to dip their toes in Venetian history.
I really enjoyed A History of Venice by Norwich. It's a history book that's presented with a lot of good storytelling, making it a good read.
It covers the entire history of the Republic, and talks a fair bit about some of the major players in Venetian history, like Genoa, Florence, the Holy Roman Empire, the Byzantine Empire, and the various crusades.