The Siege of Malta by Ernle Bradford (1961) is the definitive account of the Great Siege of 1565, written with the knowledge that Bradford had first-hand experience of Malta's second great siege — he was a Royal Navy officer in the Mediterranean during World War II. The book reads fast and gives essential context for understanding everything you see in Valletta.
Island in the Sun by Quentin Hughes (1969) is an architectural study of Malta that remains the clearest guide to what you are actually looking at as you walk Valletta's streets. Hughes traces the development of Maltese Baroque from the arrival of the Knights through to the British period, with particular attention to the city's planning and fortifications. Out of print but findable secondhand.
The Kappillan of Malta by Nicholas Monsarrat (1973) is a novel structured around Malta's history from the 1565 siege to the 1942 siege, told through the story of a Maltese parish priest. Monsarrat lived on Malta for years and the book is genuinely rooted in the island's character. It is the most-read fictional account of Malta and earns its reputation.
On the Rocks by Nicholas de Piro, the current Marquis of Casa Rocca Piccola, is a memoir about Malta and about his family's four-hundred-year connection to Valletta. It is partial, aristocratic, and charming — a perspective that no conventional guidebook would offer.