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The mountain Mount Titlis has a glacier on the top and a splendid view.
Get a beautiful view over the Mittelland and its lakes on this 2-hour walk. Go there by boat (Lucerne-Kehrsiten) and funiculaire or by train and bus (Lucerne-Stansstad-Bürgenstock). There are some luxury resorts at Buergerstock. It's also possible to go by mountain bike to the top.
A famous mountain overlooking the city of Lucerne. Pilatus is definitely a must and gives you a good impression of a wild and rocky peak with a marvelous view of the "real" Alps. Its peak can be reached by the world's steepest cogwheel railway from Alpnachstad (not operating in wintertime) and all-year-round by cable-car in three sections from Kriens (10 minutes by trolley bus no. 1 from Lucerne as far as 'Linde/Pilatus'). Going up from Alpnachstad and down to Kriens, combined with a boat ride from Lucerne, is called the Golden Round Trip and is over €100. A pleasant, and cheaper, option is to take the train from Lucerne to Alpnachstad (roughly €8), then take the cogwheel railway to Pilatus's peak and then the first cable-car down towards Kriens (roughly €52, or €26 with a rail card), and then hike the rest of the way down to Kriens (free, approximately 2 hours). Of course you can walk the entire way to the top on foot, which takes at least 4 hours from Kriens. In addition to hiking, there are several other activities, including a suspension rope park and a 1,350 m long toboggan (both at the second stop of the cable-car from Kriens). Even if you don't plan to hike, allow for at least three hours to spend on Pilatus.