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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 place themselves to the left of social democracy, which they see as insufficiently left-wing. The two main sub-types are called the radical left due to their desire for fundamental change to the capitalist system while 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, as political scientist of Marxist background Serge Cosseron, will limit the scope to the left of the French Communist Party, but there is no real consensus. Many leftists with strong anti-American, anti-globalization, opposition to NATO and rejection of European integration opinions try to avoid the negative and reductive impression associated with the far-left categorization by using the parable la gauche de la gauche ("the left of the left"), reflecting what some might view as a cultural ambiguity.
A number of far-left parties gave birth to militant organisations in the 1960s and 1970s, such as the Red Brigades and the Red Army Faction, that were active in the late 20th century. These groups generally aimed to overthrow capitalist systems and replace them with socialist societies.