Before Marx—The Utopian Years
It may surprise many of you to know that socialism and communism were not invented by Marx. And it may surprise you to know that anarchism isn't just an absolute libertine free-for-all. So let's discuss some notable historical tendencies prior to Marx and their consequent impact on the movement. We're going to start in the 18th century, since applying the label of "socialist" to historical movements of the past is a waste of time.
Fourierism
This is an odd little branch of socialism that is where I'm going to start, because it's typical of the Utopian line and had major influence by way of its publications. An invention of Charles Fourier, this socialism was deeply mystical. Based at least in part on highly esoteric readings of the Bible, Fourierism promoted the ideals of communal living and letting people pursue their own desires as part of stages of societal development. Fourier thought he'd discovered a fundamental type of social attraction, and that society would naturally begin to develop into societies of free association in forms like cooperatives where people would decide what to do through the nature of free association. Fourier was not remotely what we'd consider a scientific or atheistic socialist. Dude believed in God and Eden straight up—and that's not remotely what I'd title the unusual aspects of his belief systems. He thought people would begin to grow tails as his socialist system was implemented, and that eventually people would start living to be a hundred and forty-four years old and creatures called anti-lions would begin to exist to help humans. Dude was wilding. One of my favorite parts about Fourierism is its connection to the occult. You see, Eliphas Levi is a major figure in European occultism, and his earliest work was first published in Fourierist journals before the French Revolution. After speech restrictions leveled off after Napoleon, Levi went back to putting Fourierist and Socialist ideas in his occult publications. Aleister Crowley claimed to be a reincarnation of Eliphas Levi and his protégé who detonated himself with Mercury Fulminate, Jack Parsons, started off as a communist before HUAC got to him. So that's a neat thing, this odd intertwining of the occult and socialism.
Blanquism
Blanquism is an incredibly important, yet little-discussed tendency within socialist thought. Blanquists were outright revolutionaries. Unlike the gentler Fourierists, they were out for blood. Blanquists were of the opinion that the people could be led to revolution by a small group that would take initial actions—the first signs of vanguardism. Louis Auguste Blanqui, the creator, basically looked at society, decided it needed to go, and said "Give me twenty good men." Blanqui's plan was simple: a highly regimented, authoritarian organization would through utmost secrecy establish a coup in the government and use the state apparatus to introduce socialist ideas. Blanqui didn't really give a damn about what socialism looked like. He needed to overthrow the bourgeois and that's all he cared about. As you might imagine, this is kind of sparse ideological ground.
So I said that Blanqui was important: why is that? Well, he became a touchstone for later Socialists. Marx and Engels considered Blanqui's socialist thought carefully when writing about communism, and "Blanquist" has been a consistent accusation levied against communist movements to this day. The focus on doing your own thing with a vanguard is not something that socialists typically see as good, because modern socialists and anarchists pin their hopes on the labor movement. And given the emphasis on a revolutionary vanguard by so many socialist movements, it's unsurprising that it becomes a touchstone for conversation.
Proudhon's Mutualism
Pierre Joseph Proudhon. The first person to call themselves an anarchist. Some would call him father of the movement. I appreciate him for his writings, though, being real, dude was turbo anti-semitic and racist. So keep that in mind. It's an unfortunate tendency in early anarchist thinkers. Contrary to the common idea, anarchy has seldom really been about having absolutely no hierarchy in society. Proudhon coined the famous phrase "Property is Theft." However, Proudhon also coined the less famous phrase "Property is Freedom." Proudhon insisted that property produced by labor was essential to liberty—but property acquired through coercion was illegitimate and begot oppression. Since the state is predicated on holding the monopoly of violence, the state represents an illegitimate influence. Instead, Proudhon advocated mutualism—people would establish systems similar to credit unions to fund each others' endeavors and a free market would exist, just one beyond capitalism. Property would be defined along lines of active use. This produces a classification of legitimate and illegitimate forms of income. If your income comes from your own labor, you're good. Income produced by rent or investments, though? No good.
So this is hugely important. The nature of property in Left thought is tremendously crucial, even for Marx, and here Proudhon's work is relevant. There's a huge distinction between private property and personal property, because they aren't the same thing. If you "own" a factory, you probably don't own it in the eyes of Socialists and Anarchists—because you aren't the one typically working that factory. The workers who work that factory own it. But, say, your toothbrush, or the house you live in? That's your property. The car you drive is your property.
Proudhon is a major advocate for worker co-operatives, and also forwarded the unfortunately-titled concept of Dual Power. It's unfortunately titled since there are two concepts called dual power in Socialist thought, and the later one is more commonly known than this earlier concept. So, in Proudhon's conception, dual power is a kind of praxis where people generate structures, economies, and resources that are parallel to the markets overseen by capitalism and the state. This has in time produced the praxis of agorism, the idea of using black or grey markets as a form of direct action. It's an uncommon stance, but the Black Socialists of America have produced a less radical praxis in the form of their advocacy for generating dual power through worker co-operatives. It remains to be seen how effective this ends up being.
Proudhon is a huge deal for anarchists. Of the earliest Leftist thinkers, he is the first to outright challenge the legitimacy of the state. While later anarchists would typically question the necessity of market systems, mutualists are widely welcomed and respected among anarchists today despite their free market tendencies.