Etymology and terminology
The word "anarchism" is composed from the word "anarchy" and the suffix -ism, themselves derived respectively from the Greek ἀναρχία, i.e. anarchy (from ἄναρχος, anarchos, meaning "one without rulers"; from the privative prefix ἀν- (an-, i.e. "without") and ἀρχός, archos, i.e. "leader", "ruler"; (cf. archon or ἀρχή, arkhē, i.e. "authority", "sovereignty", "realm", "magistracy")) and the suffix -ισμός or -ισμα (-ismos, -isma, from the verbal infinitive suffix -ίζειν, -izein). The first known use of this word was in 1539. Various factions within the French Revolution labelled opponents as anarchists (as Maximilien Robespierre did the Hébertists) although few shared many views of later anarchists. There would be many revolutionaries of the early nineteenth century who contributed to the anarchist doctrines of the next generation, such as William Godwin and Wilhelm Weitling, but they did not use the word "anarchist" or "anarchism" in describing themselves or their beliefs.
The first political philosopher to call himself an anarchist was Pierre-Joseph Proudhon, marking the formal birth of anarchism in the mid-nineteenth century. Since the 1890s and beginning in France, the term "libertarianism" has often been used as a synonym for anarchism  and its use as a synonym is still common outside the United States. On the other hand, some use libertarianism to refer to individualistic free market philosophy only, referring to free market anarchism as libertarian anarchism.