Magdeburg sits on the Elbe in Saxony-Anhalt — one of the most historically important cities in Germany and, by most measures, one of the least visited by foreign tourists. The city's significance comes in waves: Otto I, who founded the Holy Roman Empire, chose it as his residence and capital in the 10th century; it was devastated twice, once in the Thirty Years' War (the Sack of Magdeburg in 1631 killed most of the population) and again in the Allied bombing of January 1945; and it rebuilt itself both times.
The Magdeburg Cathedral, begun in 1209, is the oldest Gothic cathedral in German-speaking lands and contains the tomb of Otto I. The Romanesque Monastery of Our Lady is the city's other great medieval monument, now serving as a museum and concert hall. The Magdeburger Reiter — a 13th-century equestrian statue considered the first free-standing such monument north of the Alps — stands in the Old Market Square (though a copy; the original is in the Kulturhistorisches Museum).
On a different register entirely, the Grüne Zitadelle by Friedensreich Hundertwasser is a deliberately outrageous piece of architecture — a pink apartment complex covered in trees and golden domes, Hundertwasser's last building before his death in 2000 and one of the most remarkable buildings in eastern Germany.
Magdeburg is also the birthplace of Georg Philipp Telemann (1681) and the workplace of Otto von Guericke, who conducted the famous vacuum-sphere experiment here in 1654 that demonstrated the power of atmospheric pressure using two metal hemispheres and sixteen horses. The city is not a place to linger for weeks, but its compressed medieval-imperial-scientific history repays a day or two of serious attention.