Black Lamb and Grey Falcon by Rebecca West (1941). The definitive literary account of Yugoslavia between the wars. West travelled through Dalmatia in 1937 and her chapters on Split and the Dalmatian coast are some of the most atmospheric writing about this part of the world — the history, the landscape, the people, the complicated sense of identity. Brač itself gets little attention but everything she writes about Dalmatia applies to it.
Croatia: A History by Ivo Goldstein (1999). A clear-headed single-volume history by a Croatian historian, covering everything from the medieval Croatian kingdom through Habsburg rule, Yugoslavia, and independence. Gives context for why the island's stone ended up in so many unexpected places, and for the various waves of refugees and settlers who shaped the population.
The Bridge on the Drina by Ivo Andrić (1945). Andrić won the Nobel Prize for this novel set on the Drina, far from Dalmatia — but it is the best single novel for understanding the long Balkan history of coexistence and conflict that shaped the whole region. Reading it before a trip to Croatia gives everything an additional weight.
Mediterranean: A Cultural Landscape by Predrag Matvejević (1999). Matvejević grew up in Mostar and eventually became a professor in Zagreb. This lyrical essay moves around the Mediterranean, examining harbours, boats, languages, and what it means to be a Mediterranean person. More philosophical than geographic, but it captures something true about Dalmatia's relationship to the sea.