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Anarcho-syndicalism is a political ideology that is a combination of anarchism and syndicalism (duh).
Under an anarcho-syndicalist system, all unnecessary public offices are abolished, and the legislative branch of the government is replaced by a council of trade unions, which run the affairs of state.
The aims of anarcho-syndicalism include the promotion of solidarity among the workers, direct action of the workers on their own behalf, and self organization of the workers and their work places (like any respectable socialist system).
Examples in the real world
The only example of an anarcho-syndicalist government that has ever existed (not to mention the only example of an anarchist government, and the only example of a socialist government that didn't objectively suck) was in Barcelona, Catalonia, during the Spanish Civil War. This did not last long before it was crushed by the fascists, however.
As a matter of fact, the anarcho-syndicalist movement remains strong in Spain to this very day through trade unions.