Definitions or subgroups?
I'll do a bit of both so you get the idea
Definitions
Anarchism is the abolition of government
Anarchism is the abolition of established government
Anarchism is the abolition of the state
Anarchism is the abolition of leaders
Anarchism is the abolition of rulers
Anarchism is the abolition of hierarchy
Anarchism is the abolition of system
Anarchism is the advocation of total self sufficiency and liberty
Anarchism is the lack of legitimized control
Anarchism is the lack of legal control
Anarchism is peace
Anarchism is love
Anarchism is communism
Anarchism is the free market without hindrance
Ect. I have heard all of those and more in my time
Subgroups
Anarcho-communism
Anarcho-syndicalism
Insurrectionary anarchism
Anarcho-pacifism
Anarcho-capitalism
Voluntaryism
Anarcha-feminism
Anarchism without adjectives
Anarcho-Technocracy
Anarcho-primitivism
You get the idea...