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The word "anarchy" is from the Greek, prefix an (or a), meaning "not," "the want of," "the absence of," or "the lack of", plus archos, meaning "a ruler," "director", "chief," "person in charge," or "authority".
And, just to state the obvious, anarchy does not mean chaos nor do anarchists seek to create chaos or disorder. Instead, we wish to create a society based upon communitarian unity and voluntary co-operation. In other words, order from the bottom up, not disorder imposed from the top down by authorities.
However, in anarchist philosophies, anarchy means an "anarchist society", that is, a society where individuals are free from coercion. Anarchists do not believe, as Jean-Francois Revel wrote in Democracy against Itself, that "... anarchy leads to despotism ... despotism leads to anarchy ..."  – that may or may not be true of "anarchy" in the sense of disorder, but anarchists do not believe that it is true of "anarchy" in the sense of anarchism.
Anarchist theories have a fundamental critique of government, a vision of a society without government, and a proposed method of reaching such a society. The details of the political, economic, and social organization of an anarchist society vary among different branches of anarchist political thought, as do the proposed means to achieve a society organized along those lines. However, there are certain principles shared by all anarchists, most notably the basic principle of non-hierarchy (in an anarchist society there cannot be any kind of social hierarchy) and its derivatives, such as the principle of equal decision-making power (all people must have equal decision-making power in an anarchist society; if some have more power than others, then a hierarchy is formed).