Madden's Venice: A New History is the best I've seen for a general audience. He's one of the leading scholars on the subject and has a wonderful handle on the vast source material. The "gold standard" in scholarship, toward which Madden tips his hat in the beginning of his book, is Chapin Lane's Venice, a Maritime Republic. It shows some of its age, but it's still quite good. It's organized thematically rather than chronologically and can be a bit hard for the layman to follow, but it's good. Norwich gets thrown around. He's part of this old guard of Oxbridge elites that graduated, went off and served in the foreign service/military, and came back and were in the position to write solid, popular histories on a variety of subjects. This is not to detract from the man's work—it's much better than most popular histories—but it is a popular history and he simply does not have the grasp of the archival sources scholars, such as Chapin Lane, have.

Although it isn’t exactly a scholarly account of Venetian history, John Julius Norwich’s A History of Venice is a very readable account of the Republic. Although Mr. Norwich does his best to make things as easy to understand as he possibly can, the book can be quite heavy at times, especially with the names of Doges as many of them share the same name. There are of course Thomas Maddens’ Venice: A New History (which I haven’t read) and City of Fortune by Roger Crowley (which works well as an introductory account).