Does this have anything to do with your upcoming AP World History exam?

If so, /r/HomeworkHelp. Or try doing a search on /r/AskSocialScience or /r/communism101 or /r/socialism or something. I don't think that the way the question is (currently) phrased is really suited for a good /r/AskHistorians topic.

communism is stateless, moneyless, classless society.

socialism is social ownership of the means of production. the people who work the machines in the factories own them collectively, and benefit equally from the products of their labor.

marxism is much more complex and does not have a simple definition. it is the scientific study of history, as well as the framework for socialist revolution (which leads, eventually, to communism). it is also the philosophy of dialectical materialism. it is wide ranging and difficult to sum up concisely.

if you have more questions about marxism, don't go to /r/communism as another user suggested. go to /r/communism101 where people will be happy to answer any questions you have. r/communism is for more advanced discussion and heavily moderated, your post would likely be deleted.

In addition to what others have posted I think it's worth noting that there is alot of diversity within Marxism. When most people think of Marxism they're usually thinking of Marxist Leninism, which includes Stalinism, Trotsky-ism, and Maoism. There is also various libertarian Marxisms (autonomism, left and council communsim), which have alot in common with anarchism. They are highly influenced by Marx's critique of capitalism but reject what they see as authoritarian tendencies in Leninism.

Marxism is the ideology founder by Karl Marx, roughly based on his ideas. There are many opinions about what those mere, but I shall give my humble opinion. Marx believed economic laws were subjective, arguing early man existed in a state of "primitive communism", wherein the tribesmen worked for the good of the band or clan to ensure common prosperity. Marx believed man would eventually return to a state similar to this. He advocated a temporary and democratic state, along with a few prescribed policies. This state would slowly implement a new economic system; where all tools, factories, and so forth were owned by the governing authorities and consumption and distribution were planned by the state. This would slowly mold the minds of people living in this new system, and society would eventually evolve to a stateless, classless, moneyless world. He believed this was an inevitability due to his idea of the Hegelian dialectic, which I am not really educated in so I shall not try to give his version.

"Communism" usually refers to Marxism, but in the 19th century it didn't have such strict usage. Many anarchists claim they are the true communists.

"Socialism" used to refer to a set of radical ideas that often overlapped with Marxism and anarchism, but it's usage has now expanded to refer to welfare state policies.

Marxism is a wider system of thought that influenced a series of academic disciplines, including sociology, philosophy and history. These disciplines may have little or nothing to do with the economic sense we consign to Marxism in the modern era. For example, in historical study, Marx was probably most famous for inverting the Hegelian model of progression by suggesting that history was not necessarily moved by a Geist, which took hold of incredibly influential politicians/states/leaders. Instead, progress was made from the "bottom-up": the proletariat in this sense wasn't simply an economic designation. The proletariat represented a series of intersections in which social and political power was denied to these individuals by the bourgeoisie. Progress was measured by the proletariat's ability to remove the obstacles and burdens from power. This is how we derive Marxist interpretations of the French Revolution, for example.

Socialism is an idea that pre-dated Marx by at least two millennia (see the reforms of Solon in 6th century Athens). The main idea behind a socialist thinker is again, more general than the economic "socialism" we picture in the present. A socialist was simply an individual who conceived the state/nation/polity as fundamentally more valuable than the individuals who comprised it. Part of the state/nation/polity was a responsibility to take care of the individuals. This is the aspect of socialist thought that was revived in the 19th century, as a response to the aggressive development of "liberal individualism" in which it was thought people ought to achieve as much as markets would allow. From this, we also derive its investment in concepts like social ownership of production, co-operative forms of labor, collective bargaining shenanigans, etc.

Communism, again is a concept that dates Marx by at least 1.8k years (there are some reasonable arguments that you can see communist thought within the Republic of Plato). For the purposes of modern thought, it generally referred to the specific employment of Marxist economic thought within the context of the Soviet states following the Revolution of 1917. These ideas drew upon the concept of the state as the only entity with claims to ownership of products, raw goods, and production. Rationing was decided by the state in order to assure that no one individual received more than any other without the state's approval.

Since it seems you are most concerned with how these topics related to Marx, I might suggest reading Marx's Capital, as well as a series of Marx-Engels readers to gain a basic understanding of these differentiations in his thought process. The one that helped me most was printed by Oxford

Karl: Marx, Selected Writings, second edition ed. David McLellan (Oxford: Oxford University Press, 2000)

-mvl