Anarchism is a set of ideas, ranging from philosophical to political to economic to sociological and further, with the common idea that unequal power relations are Bad Things. Different anarchists say different things about exactly how or why hierarchical structures are bad, how they should be abolished, and even what constitutes a hierarchy, but all
1 agree that they should, whenever possible, be avoided. Indeed this is simply the etymology of the word "anarchy", which is derived from the Greek word "anarchos", meaning "without ruler", and not having rulers is essentially what anarchism is about.
As a theory, anarchism had its beginnings in the middle of the 19th century. Anarchistic thoughts can be seen much earlier, such as in the writings of Gerrard Winstanley, and some trace anarchistic writings as far back as the Stoic philosopher Zeno of Citium (though I haven't read anything particularly anarchist in Greek writings yet). Most agree that four men in the 19th century set out basic anarchist thought: Pierre-Joseph Proudhon, Max Stirner, Mikhail Bakunin, and Peter Kropotkin. They didn't so much invent anarchism as much as give a theoretical basis for anarchist ideas, fleshing out concepts that had been tossed around society for who knows how long, probably since the ideas of social power and authority were first conceived (invented or recognized). They didn't all agree with one another either-Stirner refutes some of Proudhon's writings in The Ego and Its Own and elsewhere. But each influenced later anarchists in various ways, even if only by way of refutations.
While spanning many spheres, anarchism is more of a philosophy, a way of looking at things, than anything else. There is no orthodoxy, as opposed to Marxism, although individual schools might be more or less dogmatic. But as a whole, anarchism can be compared to the philosophy of the Greeks, who saw their actions guided by their philosophies. Anarchism is a way of approaching the various facets of life, social and individual, and it is generally agreed that anarchism is useless without practical applications; most anarchists are activists in one way or another. Many anarchists, though definitely not all, embrace the variety of interpretations; one could only think that, "after the Revolution", there would not be one society but a multitude, all living out anarchistic ideas in their own ways.
Next week: Proudhon's views on property
1 I use "all" in this sense as meaning all who self-identify as anarchists. However, this is not quite true; there is, in fact, a set of ideas called "anarchocapitalism". It is a variant of right-wing libertarianism, the economic ideal of which is a completely free market with no government to interfere with it. All industries, all services, would be privately owned. They take "anarchism" as meaning strictly "no government", where all other anarchists (to my knowledge) take it in the more general sense of "no rulers" or "no authority" of any kind.