Magdeburg's most striking monument is its cathedral — the oldest Gothic cathedral in Germany and the burial place of Emperor Otto I. The cathedral stands on a bluff above the Elbe, surrounded by a modest park, and its two towers dominate the city's skyline. Otto I chose Magdeburg as his residence and made it the center of his empire's religious administration in the 10th century, and the city's role as an imperial seat explains much of what you see here.
The other major monument, the Romanesque Monastery of Our Lady (Kloster Unser Lieben Frauen), has been deconsecrated and functions as a museum and concert hall — the acoustics are excellent and there are regular chamber music events. The Kulturhistorisches Museum, housed in a former palace near the cathedral, covers the city's long history from prehistoric times through the Thirty Years' War and the Second World War.
For the unusual, Magdeburg has the Grüne Zitadelle — a Friedensreich Hundertwasser building that looks like a pink wedding cake that's been partially digested by a forest — and the Jahrtausendturm in the Elbauenpark, a wooden tower packed with hands-on scientific experiments.