Depends on what you mean by, "far left." The left/right divide in politics comes from the French Revolution, wherein the members of the French National Assembly divided into those who supported the king and the nobility (the right half of the chamber) and those who supported liberalism and rights and freedoms for the people (the left half of the chamber). Liberalism was a relatively new political idea at this time, the concept that average people should deserve political rights and freedoms was completely new, since the nobility and royalty had governed Europe by the divine right of god and with the support of the church for a thousand years.

This is also where the political meaning of the word, "radical," comes from. A radical is somebody who does not like an existing political system, and wants to replace it with a new system. People like the French or American liberals during the French and American revolutions wanted to replace the old monarchy and nobility with liberal political freedoms for all citizens. The United States and Modern France were both literally founded by radical liberals. Do keep in mind that back then, in order to be a citizen, you needed to be a white male over the age of 21 who owned a house or land. You could not be a citizen if you were non-white, if you were non-male, if you were under 21, were homeless, were a travelling worker, or rented your home form a landlord.

People like Thomas Paine in the US or Robespierre in France were considered the far left of their time, since they were liberals who believed in a government that benefitted the people rather than an upper elite.

The industrial revolution came to different parts of the world at different times, but by the point around the 1820s when the industrial revolution was underway western Europe and some parts of North America is when the first socialists emerged. The original goals of liberalism were to use individual rights, property rights, and individual freedom of choice to maximize human freedom. Since giving property rights to individuals would allow more people to be free and serve their government for the benefit of all, individuals believed that property rights were the best way to achieve economic prosperity. This was a radical idea when for a thousand years it was the king or the nobility to controlled all property, and could give or take anything at will. The first socialists were radical liberals who believed in the goals of liberalism (maximizing human freedom) but who believed that property rights failed to do this, since it allowed small groups of people to hoard massive amounts of wealth and use their wealth to control others. The first socialists attempted to create communities where instead of property belonging to individuals, property belonged to the community at large, and people democratically voted on how to use it. Look into people like Robert Owens, Henri Saint-Simone, Pierre-Joseph Proudhon, and others. None of these original socialist projects worked, because they never got enough support to function, or were crushed by the military and police in their areas as threats to the established liberal states.

Then Marx came along in the 1840s, and many of Marx's earlier writings were devoted to explaining why those liberal socialist projects had failed, and why their underlying philosophy was flawed. The discussion of Marxist philosophy is a huge topic, but Marx' goal was twofold - to create a new philosophy which allowed for a better analysis and understanding of how societies, economics, and politics all function, and to use this new philosophy to explain how a better post-capitalist and post-liberal society might be achieved.

While Marx has had an undeniable influence on much leftist thought, it is important to remember that the global left is extremely diverse. Even while Marx was alive, there was a great split in the European socialist movement between Marxists who wanted to use the state as a temporary tool to create a socialist society, and the Anarchists who believed that the state needed to be abolished immediately in favour of directly democratic unions and coalitions. By the time that Lenin and his followers formed the Soviet Union in 1922, Marx had been dead for decades, and it is still hotly argued over by historians and philosophers whether or not Marx would have supported what Lenin did. By the time that Stalin ruled the USSR, Marx's original works were being censored because Stalin viewed them as a threat to his power. Today you have millions of leftists around the world with a very broad range of ideas. Leftist infighting is a meme because leftists tend to be very passionate and free-thinking, and disagree over the best way to achieve socialism or what socialism even means.

I don't want to discourage other people from answering, but somebody asked a similar question quite recently and got what I thought was a pretty good answer by u/TheExquisiteCorpse.

I just wanted to build upon earlier comments in this thread:

Marx coined the term 'utopian socialism' to describe many of the socialist and anarchist movements that emerged in the 18th-19th centuries. Utopian socialists appealed to abstract moral principles in their critiques of capitalism and in their theorizing about the ideal society. The movements inspired by Charles Fourier (Fourierists), Henri de Saint-Simone (Saint-Simonists), and Robert Owen (Owenites) fall under the banner of utopian socialism. Similarly, Ricardian socialism drew upon the economic theory of David Ricardo, specifically his theory of embodied labour, to criticize capitalism. Important Ricardian socialists include Thomas Hodgskin, William Thompson, and John Gray.

Pierre-Joseph Proudhon, famous for his claim that property is theft, was an influential radical in mid 19th century France. In The Poverty of Philosophy, Marx offers a scathing and lengthy critique of Proudhon's brand of anarchism. What's more, another important French radical around the same time, Louis Auguste Blanqui, believed that a coup-based dictatorship led by an elite clique of radicals is necessary and sufficient for building a just society.

The left-wing Young Hegelians played an indispensable role in the development of Marx's thought. Based on their interpretations of Hegel's dialectics, the Young Hegelians argued that humanity has yet to reach the end of history, given the need to overcome the contradictions (or internal tensions) inherent in monarchism, inegalitarianism, and the marriage of religion and state. Important Young Hegelians include Bruno Bauer, Max Stirner, and Ludwig Feuerbach, especially since their work features heavily in Marx's The German Ideology. Feuerbach's The Essence of Christianity, which offers a materialist critique of religion, heavily influenced the development of Marx's dialectical materialism and theory of alienation.