Rejection of coercive authority can be traced as far back as Ancient China, where Taoism is declared by some to have been the oldest example
of anarchist doctrine [1].
In the West, a similar tendency can be traced
to the philosophers of Ancient Greece, such as
Zeno, the founder of the Stoic philosophy, and Aristippus, who said that the wise
should not give up their liberty to the state [1].
Later movements -- such as the Free Spirit in the Middle Ages,
the Anabaptists, The Diggers and The Levellers
-- have also expounded ideas that have been interpreted as anarchist.
It can also be conjectured that in past times, many people were anarchists but did not have the opportunity to get such ideas openly published, and that many people did have anarchist fancies but did not dare take them seriously.
See for instance how La Boétie, in his essay against tyranny,
doesn't dare deny legitimacy to the reigning monarchy of his time.
The first known usage of the word anarchism seems to be traced to the French Revolution (c.1789), when it was used as a derogatory term against the left.
The first author to have published a treaty explicitly advocating
the absence of government (without using the name anarchism)
seems to be William Godwin, in 1793.
The French philosopher Pierre-Joseph Proudhon,
in the 1840s, is considered to have been the first
to refer to oneself as an "anarchist",
which he did in a non-derogatory fashion,
becoming the first to articulate a social philosophy
that called itself anarchism.
He referring to anarchy as absence of government.
Proudhon was a socialist,
though he incorporated some classical liberal ideas in his discourse. He became fiercely anti-communist with pronounced anti-semitic and nationalist views.
Bakunin and many others, particularly in Europe,
have developed after Proudhon an anarchist movement
that openly endorses the main socialist ideas and left-wing politics.
Benjamin Tucker, who translated Proudhon into English,
insisted on the individualist aspect of anarchism. He and others clearly advocated free markets as solutions
to problems government claimed to solve, though they soundly rejected usury, wage-labor, and capital.
Though Tucker and other similar authors also claimed
the unqualified term "anarchist",
they are often called individualist anarchists
to disambiguate when needed.
The Development of Anarchism before the nineteenth century
Proudhon and later
Later development
Alongside the popular development of socialism in the nineteenth and twentieth centuries, anarchism developed through many stages.