Definition
Anarchism is defined as a political theory in which society should have no government, rejecting compulsory governance and supporting its elimination.
Origin
The origins of Anarchism go back to Britain, in the late 18th century. An important anarchist philosopher, William Godwin, believed that the “euthanasia of government” would be achieved through “individual moral reformation”. Godwin however, did not give the name ‘anarchism’ to the ideas he developed. Godwin advocated extreme individualism and proposed that cooperation in labor be eliminated.
It was only after Goldwin’s death that the term “anarchist” was coined by Pierre-Joseph Proudhon. He wrote a book, ‘What is Property?’, which incorporated a deeper meaning to the word ‘anarchism’, becoming not only a rejection of established authority but also a theory opposing ownership of land and property. He also saw anarchy as “a form of government or constitution in which public and private consciousness, formed through the development of science and law, is alone sufficient to maintain order and guarantee all liberties. In it, as a consequence, the institutions of the police, preventive and repressive methods, officialdom, taxation, etc., are reduced to a minimum. In it, more especially, the forms of monarchy and intensive centralization disappear, to be replaced by federal institutions and a pattern of life based on the commune”.

Schools of Thought
There are a number of schools of thought under Anarchism. They are: Mutualism, Collectivist anarchism, Individualist Anarchism, Anarchist Communism, Anarcho- syndicalism, Anarcho- capitalism, Green anarchism and Anarchism without adjectives
Mutualism
What Mutualism is about is receprocity, free association, voluntary contract, federation, and credit and currency reform. A large number of mutualists believe that a market without government intervention will drive prices to labor-costs, eliminating profit, rent, and interest according to the labor theory of value. Firms would be forced to compete over workers just as workers compete over firms, raising wages.
Collectivist Anarchism
Collectivist Anarchists basicly oppose all private ownership of production, advocating that ownership has to be collectivized. However, the collectivization is such that workers will still be paid according to time worked, not receiving goods being distributed "according to need".
Individualist Anarchism
The main idea of Individualist anarchism consists of "traditions" that suggest that individual conscience and self-interest should not be controlled by any collective body or public authority. It also supports of property being held privately.
Anarchist Communism
Anarchist communists feel that a society should compose of a number of self-governing parties with collective use of the means of production and direct democracy as the political organizational form. In anarchist communism, individuals do not receive direct compensation for labour, but would instead have free access to the resources and surplus of the commune.
Anarcho- Syndicalism
Anarcho-syndicalists seek to abolish the wage system and private ownership of the means of production, which they believe lead to class divisions. Important concepts of syndicalism include workers' solidarity, direct action in the form of strikes etc., and workers' self-management.
Anarcho Capitalism
Anarcho-capitalism is a political philosophy "based on a belief in the freedom to own private property, a rejection of any form of governmental authority or intervention, and the upholding of the competitive free market as the main mechanism for social interaction."
Green Anarchism
Green anarchism is a school of thought which puts particular emphasis on the environment. Primitivist and anti-civilization green anarchists advocate a return to a pre-industrial and usually pre-agricultural society.
Anarchism without Objectives
Anarchism without adjectives emphasizes harmony between various anarchist factions and tries to unite them around their shared anti-authoritarian beliefs.
References
A.1 What is anarchism?. (n.d.). Retrieved Mar. 22, 2008, from http://www.geocities.com/capitolHill/1931/secA1.html.
Anarchism - Definition from the Merriam-Webster Online Dictionary. (n.d.). Retrieved Mar. 22, 2008, from http://www.merriam-webster.com/dictionary/anarchism.
Anarchism - Wikipedia, the free encyclopedia. (2008, March 22). Retrieved Mar. 23, 2008, from http://en.wikipedia.org/wiki/Anarchism .
Anarchism. (n.d.). Retrieved Mar. 23, 2008, from http://www.spartacus.schoolnet.co.uk/USAanarchist.htm.
Justice , J. (n.d.). Defining Anarchism. Retrieved Mar. 22, 2008, from http://flag.blackened.net/liberty/defanar.html.
Index of anarchists and anarchism around the world. (n.d.). Retrieved Mar. 23, 2008, from http://flag.blackened.net/revolt/anarchism/index.html.