You wanted to learn about anarchism, allow me to explain:
Anarchism is the political theory which supports the abolition of authoritarian systems and replacement of these with libertarian systems. The government is an authoritarian institution, therefore it must be abolished, giving way to a horizontal form of organization where there is no hierarchy.
Anarchists don't agree to with the dictatorship of the proletariat, because if we don't abolish the state and change into anarchy immediately an authoritarian government might rise.
We beleive (at least anarcho-communists do) in a system that works like communism, it is stateless, it is money-less, workers self-management, abolition of private property, direct democracy; the diference is we don't like the idea of a transition state, and we call our end goal anarchy (not communism).
If you have any questions ask me, I would be happy to answer them all.