The summits
There are 52 countries (including sovereign nation) part of the European continent as defined by the historical and cultural rule: Europe is separated from Asia by the Ural Mountains, the Ural River, the Caucasus Mountains, in south east by the Caspian Sea and the Black Sea.
52 countries for 50 summits, since France and Italy share Mont Blanc, and Albania shares Mt Korab with Macedonia.
Note: Only countries or sovereign states are part of the list. This explains for example the presence of Monaco (a sovereign city-state), and not the Island of Jersey (a crown dependency).

For countries on the border, such as Russia, Georgia or Azerbaijan, their highest peaks are still considered to be in Europe. For Turkey, the highest peak being in Asia, the highest European peak has been selected instead.
Cyprus being part of the European Union has also been included in the list despite being technically in the Middle-East.
Also to be noted: although a small part of Kazakstan is technically within Europe, there are no recorded high point on that flat part of land.