It also occupies one of the most disputed patches of real estate in Europe, coveted, fought over but miraculously spared by the Poles, the Romanovs, the Hapsburgs, Hitler, Stalin and the Ukrainians themselves. History in this part of Europe is less a matter of dates and events than lines and shading on maps.
Bogdan Tchaikovsky, director of the Lvov - or Lviv - Historical Museum, says there are so many different maps in the museum's collection no one has had time to count them. For most of his 15-year stint as director, they collected dust in the cellar. The only map that mattered was fixed at Yalta in 1945. It put Lvov and the rest of Galicia firmly in Ukraine and Ukraine firmly within the borders of the Soviet Union.
Slowly the old maps are coming out. The museum starts with a diagram of Kiev's domain in the 9th century. Moscow is not even a blob. Later comes an 18th century English cartoon showing the Russian and Hapsburg monarchs redrawing the map of Central Europe. More recent carve-ups, though, are absent. An entire wing of the museum - a magnificent Italianate mansion first built for a 17th century wine merchant - is in the throes of a Soviet-style revision which started when Ukraine became independent in 1991.
'Politics still intrude,' complains the director. 'Before it was the Party, now others want to tell us what to say.'
And when it comes to frontiers, nearly everyone in Lvov seems to have something to say. In Soviet times, secrecy conspired with dogma to make maps either wrong or non-existent. (For years the best map to Moscow was published by the Central Intelligence Agency. It gave all the streets and buildings which, for one reason or another, had been deleted from Soviet maps).
In western Ukraine cartography is something of an obsession. On Freedom (formerly Lenin) Prospekt, Lvov's main bookshop sells pots and pans as well as literature but its most popular line seems to be maps. I bought four different versions of Ukraine, three of Lvov and a world political map enshrining Ukraine as an independent state. All had been printed since independence. While much of Ukraine's industry has ground to a halt its map factories must be working non-stop. It as if people need reassuring that the impossible really did happen. They want it confirmed with a splash of pale- green ink for Ukraine, instead of a great band of Soviet pink, designated in one corner with the tag Soviet Socialist Republic of Ukraine.
The reverence for - and manipulation of - maps reaches its apogee with Lvov's politicians. 'Everyone puts up the map that suits their own purposes,' says the museum director. At the headquarters of Rukh, an umbrella movement that galvanised support for independence, maps of Ukraine share wall space with more detailed maps of Crimea, the contested peninsula in the Black Sea. This is a bit of Soviet cartography Ukrainian patriots like: a decision by Khrushchev in 1954 to redraw the borders so as to remove Crimea from Russia and present it as a 'gift'. Stalin's success at forcing Poland to hand over most of Galicia and Volhynia is also welcomed, so long as it is Ukraine and not the Soviet Union that profits from the Great Dictator's bullying
More imaginative and more dangerous nationalists have their own ideas about cartography. Among those wanting to reshape the world is the editorial staff of Our Nation, a neo-Fascist journal that offers tips on paramilitary training and gun-care. A world map in the corridor outside the editor's office has been revised to include a few modest changes: Ukraine occupies the entire former Soviet Union; most of Western Europe has become the 'dependent territory of Ukraine'; the eastern seaboard of the United States, including Washington and New York, has been renamed the 'New States of Ukraine'. Only Canada, blessed with a large population of Ukrainian immigrants, is spared.
I can find no trace of Russia, which seems to have vanished entirely, but I am searching in the wrong place. An activist from Our Nation points me in the right direction. In the Central African Republic there is a circle of barbed wire; scrawled in the middle is a tag to identify its inhabitants: the Russians. This, says Our Nation, is a joke.