Lucerne

A roofed timber bridge from the 1330s, with a painted panel of city history fitted into each triangle under the roof. Fire took most of them in 1993, and a few were hung back scorched instead of restored, so the reach of the fire is still readable.

Nine towers joined by wall run along the ridge above the old town, and several can be climbed inside. The clock tower strikes one minute before every other clock in the city, a right it has held for centuries. The stairs open in spring and shut as autumn ends.

Not a statue set up but a figure cut into the rock face. It stands for the Swiss guards who died defending a palace in Paris in 1792. The lion, a spear in its side, keeps a paw over a shield. The pool in front is small and a crowd has no room to step back.

At its steepest the rack takes a forty-eight per cent grade. The seats are stepped and tilted into the slope, so a passenger keeps one posture the whole way. It does not run while snow lies, and the far side must be used instead.

Steam engines and aircraft came in whole rather than cut down, so the halls feel like a hangar. The gear that bored the Alpine tunnels stands in the middle of one. Avalanches are demonstrated next door. Much can be handled, so wet days fill it by mid-morning.

A few boats still on the lake's scheduled runs are older than a century. Glass over the engine room lets the deck watch the pistons work, and the smell of oil comes up with them. Tickets do not name the boat, so the mark on the timetable decides the sailing.

The lower bridge draws fewer people, so its panels can be read slowly. What hangs here is not city history but death taking rank and beggar alike, and the weir alongside once set the level of the river.

One family's pictures hang in a former bank building: Picasso was close to them in his last years, so photographs of the household sit beside the paintings, and the lower floor is given to small works on paper by Klee.

The roof of the lakeside hall runs far past the building and out over the water. Nobody gets wet underneath it, so people stand and wait there, and from the lip the sky is cut into a frame above the lake.

An inner square of the old town, quieter than the riverside, with painted fronts on the houses around it. The figures in the paintings hold whatever that house sold, which is what a shop sign was before lettering. The well in the middle still runs.

In 1871 a rack railway climbed from Vitznau, the first mountain railway in Europe. The usual loop is boat from Lucerne to Vitznau, train up, and descent on the opposite flank to Arth-Goldau. Near the summit several lakes lie below at once.

A glaciated peak reached by train to Engelberg and a chain of cable cars. On the final gondola the floor rotates, swinging the view full circle as you rise. Up top are an ice cave and a suspension bridge over a cliff, with snow lying even in midsummer.

A double-decker cable car from 2012 whose upper deck has no roof, so you ride up in the open wind. From the village of Stans an old funicular runs to the midway station first. A short loop round the summit takes in lakes and Alps alike.

A steel-frame lift built in 1905 on the outside of the Burgenstock cliff, rising up bare rock above the lake. Boat and funicular from Lucerne reach the resort, then a ledge trail along the rock leads to its foot. Up top, Lake Lucerne branches every way.

Right beside the Lion Monument, digging for a house in 1872 uncovered round holes ground out by glaciers. They are shown under a roof now, and the same ticket lets you into an old hall of mirrors. With the lion next door, an hour covers both.

Twin onion-domed towers rise on the left bank of the Reuss: the first large Baroque church in Switzerland north of the Alps. Inside, white walls, pink marble columns and gilding glow bright. From the old town across the river, its reflection looks loveliest.

Wagner lived in this lakeside house for six years from 1866, and the Siegfried Idyll was first played on its stairs on his wife's birthday morning. It is a small museum of his piano and letters now. Walking along the shore from town takes about 30 minutes.