The Dresdner Schwebebahn is easy to miss if you don't know to look for it, but it is one of the most unusual pieces of public infrastructure in Europe. A single suspended rail car hangs from an overhead track and climbs 1.6 kilometres from Loschwitz on the Elbe valley floor up to Oberloschwitz on the ridge above, rising 84 metres through the trees. The views over the Elbe and the Dresden skyline are excellent.
The railway opened in 1901, making it the oldest suspension railway in the world. It was built to connect the prosperous hilltop suburb of Oberloschwitz with the river and the city below. The technology — cars hanging from an overhead monorail rather than running on rails below — was genuinely novel, and Dresden's version predates the Wuppertal Schwebebahn by about a year. Both have been running continuously ever since.
The Schwebebahn is part of Dresden's regular public transport network (DVB), so you ride it on a standard transit ticket. From the Loschwitz terminus it's a short walk to the Elbe meadows and the Körnerplatz, a pleasant square with cafes. From Oberloschwitz, paths lead through the hillside woods toward the Dresdner Heide and the Blaues Wunder bridge below.
The Blaues Wunder (Blue Wonder) — a cantilevered iron bridge from 1893 that spans the Elbe nearby — is worth seeing while you're in the neighbourhood. It survived 1945 undamaged partly because a German officer refused the order to blow it up.