Individual freedom, voluntary association, and opposition to the state are important beliefs of anarchism. There are also big differences between anarchist philosophies on things like whether violence can be used to bring anarchy; the best type of economy; the relationship between technology and hierarchy; the idea of equality; and the usefulness of some organization. The word "authority" is not clear, but anarchists are not against some types of authority (e.g. the authority of someone skilled in self-defence over someone that wants to learn self-defence), they are only against human domination.
There are many anarchists who reject capitalism and support socialism or communism (but in another sense, without a totalitarian state or power), they are called anarcho-socialists and anarcho-communists. Also, there are some people called anarcho-capitalists who oppose government, but support capitalism (but in another sense, neither corporatist government nor state capitalism), although many of them are okay with socialism between consenting participants, as long as they don't force them into the socialist system. Other anarchists say that they are not really anarchists, because anarchism is traditionally a socialist philosophy. Finally, there are "anarchists without adjectives" who hold that because people will be free in an anarchy to pursue voluntarily any economic structures they want (including communes, worker co-ops, and capitalist-owned firms). Anarcho-socialists and anarcho-communists believe that people can voluntarily participate in socialist/communist systems without having to be forced to, unlike their authoritarian counterparts that believe everyone should be forced into their system whether they like it or not.