Pskov Chronicle (medieval primary source, various modern editions) — the chronicle kept by Pskovian monks from the 13th to 16th centuries is the primary source for the city's history as an independent republic. Translated excerpts appear in anthologies of medieval Russian sources. Dry but revealing about how the city governed itself and conducted relations with its aggressive neighbours.
A History of Russia by Nicholas Riasanovsky — the standard English-language survey of Russian history covers the medieval republic period and gives context for Pskov's significance as one of the two great city-states (alongside Novgorod) that operated independently before Moscow's rise.
The Icon and the Axe by James Billington — a cultural history of Russia that gives sustained attention to the icon-painting tradition, including the Pskovian school. Required reading for anyone who wants to understand why the flat, golden images in Pskov's churches look the way they do.
Alexander Nevsky (1938 film, dir. Sergei Eisenstein) — not a book, but essential viewing before or after a visit to Pskov. Eisenstein's film about the 1242 Battle of the Ice, with Prokofiev's extraordinary score, captures something of the medieval northwest Russian world even through its Soviet-era distortions. The battle took place on Lake Peipus, visible from the area around Pskov.