The Alps are divided among the following countries:
Austria, Slovenia , Switzerland, Liechtenstein, Germany, France, Italy and Monaco.
Italy has the largest part of the Alpine territory (32%).
instead, France Switzerland and Austria, all together, represent 55% of the Alpine territory.
However it’s possible that many American people think that Switzerland is the only one related with the Alps because, from a strictly national point of view, the Alps are only dominant in Austria (65,5% of its territory) and Switzerland (65%), while French and Italian territories are very diversified in terms of territory identity.
Moreover these two countries have other mountain ranges (Pyrenees in France and Apennins in Italy)
Innsbruck is called "the capital of the Alps" because it's the biggest city in the Alps range and is located in the middle of them.
In my opinion the best ski domain in the Alps is Matterhorn Ski-Paradise. It covers the ski resorts of Cervinia (ITA) and Zermatt (SWI) and it has 313km of slopes.
Other fantastic ski towns/resorts:
Val d'Isere (FRA), Chamonix (FRA), Kitsbuhel (AUS), Cortina (ITA), St. Moritz (SWI)
While the most wonderful mountain range are the Dolomites, in North-Eastern Italy.
They are an UNESCO World Heritage Site
http://www.youtube.com/watch?v=DKuYDJ5wL0k