This page is about politics. In case it is never updated, I'll throw down some cursory ideology.
Hierarchies are the ranking of categories of person, generally resulting in double-standards or unfair treatment. For instance, gender as a hierarchy might look like a woman having difficulty finding a job due to stigmas against women in the workplace.
People occupy multiple categories at once. Albert is a white trans man. Bob is a black trans man. Both may experience the oppression of their gender differently. Albert may act to dismantle the hierarchy of gender by supporting trans rights. Bob may perform the same acts, albeit face additional challenges from being black. The two hierarchies at play do not work separately, but combine. When seeking allies, Albert will have an easier time than Bob, who may face discrimination from Albert's allies. In this way, hierarchies enforce one another. It is therefor wise to resist as many hierarchies as one is aware of.
Expertise is the means by which one entity may consensually defer to another. You ask your friend who's good at construction to help you renovate your home and improve safety. He recommends tearing your entire house down and building from scratch. You thank him for his advice, and consider whether you should follow it. If you decide to follow it, you extend your consent to his decision. If you refuse, you safely revoke your consent.
Authority is the means by which one entity robs another of autonomy. A state housing inspector deems your house unfit to live in. You can decide to heed this assessment as wise advice. If you refuse it, however, the force of the law will be brought upon you. A state may give fines, and if those fines are in turn ignored, it may send a police officer to abduct you, and if you resist this abduction, deadly force may be used to subdue you. Penalties don't need to include death. Any penalty or power differential can be used to prop up authority.
"There is no anarchy, only anarchists." This will hopefully seem obvious, but anarchy is not a form of government. The notion of anarchy as some utopian state where all hierarchies are permanently dismantled is ridiculous, and not just because a state is a form of hierarchy. As long as there are people, there will be a struggle between the dismantling and preservation of hierarchies. The imagined utopia in actuality would be, like the current day, requiring anarchists to resist the hierarchies. So the apocalypse myth of great struggles leading to an eternal utopia can be discarded. Instead, we must live in the here and now. It is an anarchist's mission to identify which hierarchies are present, and in what ways they can be resisted here and now.
The ideal means of reaching goals is the one that weakens hierarchies instead of reinforcing them. This has the benefit of making the pursuit of your goals inherently revolutionary. Likewise, if you bypass existing institutions and organize directly with your comrades, you are not tied down to the rules that govern those hierarchical institutions. If you don't ask permission, you can't be pre-emptively denied. If you can solve a problem without using money, it is much harder to tax you. If your org lacks a central leadership, it is much harder to coopt or undermine. If your platform is the word of mouth, it is much harder to be deplatformed. Becoming ungovernable in your actions is half the fight. When you operate outside the bounds of state, capital, race, and gender, you undermine them.