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Luke March of the School of Social and Political Science at the University of Edinburgh defines the far-left in Europe as those who position themselves to the left of social democracy, which they see as insufficiently left-wing. The two main sub-types are called the radical left, who desire fundamental changes to the capitalist system yet remain accepting of liberal democracy, and the extreme left, who are more hostile to liberal democracy and denounce any compromise with capitalism. March specifies four major subgroups within contemporary European far-left politics: communists, democratic socialists, populist socialists and social populists.
Vít Hlou?ek and Lubomír Kope?ek add secondary characteristics to those identified by March and Mudde, such as anti-Americanism, anti-globalization, opposition to NATO and rejection of European integration.
In France, the term extrême-gauche ("far-left") is a generally accepted term for political groups that position themselves to the left of the Socialist Party, such as Trotskyists, Maoists, anarcho-communists and New Leftists. Some, such as political scientist Serge Cosseron, limit the scope to the left of the French Communist Party, but there is no real consensus.
There were many far-left militant organizations formed from existing political parties in the 1960s and 1970s, such as the Red Brigades and the Red Army Faction. These groups generally aim to overthrow capitalism and the wealthy ruling classes.