No other city of its size sits this close to real mountains. From the Golden Roof in the middle of Innsbruck, a funicular and two cable cars take you to 2,256 m in about half an hour, into the Karwendel, the biggest nature park in Austria, and in winter you can be skiing before the shops open. The name means "bridge over the Inn", and the town grew up at the river crossing on the road between Germany and Italy over the Brenner Pass, which is still its reason to exist.
For a while it was one of the capitals of Europe. Emperor Maximilian I, the Habsburg who married his way into half the continent around 1500, loved it more than Vienna, and left it a golden balcony and the most extraordinary tomb in the Alps, which he isn't buried in. Later came Maria Theresa, a peasant uprising against Napoleon in 1809 that made an innkeeper called Andreas Hofer Tyrol's national hero, and two Winter Olympics, in 1964 and 1976. Today it's a university town of about 130,000 people, and the mix of baroque streets, Zaha Hadid buildings and climbers carrying ropes to the tram is what makes it different.
Day one is the old town and the Habsburgs, day two the Nordkette and the Alpine zoo, day three Bergisel, Wilten and Maria-Theresien-Strasse, day four Hall in Tirol and the Swarovski Crystal Worlds, and day five a high walk on the Patscherkofel and Ambras Castle. For the rest of the country, see Austria.