Short answers, pulled from the story.
Marxism is a political philosophy and method of socioeconomic analysis that uses historical materialism to understand class relations and social conflict. It views class struggle as the central driving force of historical change and treats a society's economic mode of production as the foundation of its social, political, and intellectual life.
Marxism originated in the works of the 19th-century German philosophers Karl Marx and Friedrich Engels. The two first met in September 1844 and co-developed communist theory together, publishing The Communist Manifesto in February 1848.
In Marxism the bourgeoisie are those who own the means of production and buy labour power, while the proletariat are modern wage labourers who own no means of production and must sell their labour power to live. Marx argued the bourgeoisie exploit the proletariat because the worker's labour generates surplus value greater than the worker's wage.
Marxism defines exploitation as surplus labour, the labour performed beyond what a worker receives in goods, and locates the source of capitalist profit in this surplus value. Alienation, or Entfremdung, is the estrangement of people from their humanity, an objective and systematic result of capitalism in which the fruits of production belong to employers.
The most prominent 20th-century school was Marxism-Leninism, developed after Vladimir Lenin's death as the official ideology of the Soviet Union and other Marxist states. Other traditions include Western Marxism, Marxist humanism born in 1932, and libertarian Marxism, which emphasises anti-authoritarian aspects and rejects the need for a vanguard party.
Marxism has been criticised for lack of internal consistency, for being a form of historical determinism, and for the economic calculation problem identified by Ludwig von Mises. Karl Popper argued it degenerated from a predictive theory into pseudoscientific dogma, while Austrian economists such as Eugen Bohm von Bawerk attacked its labour theory of value.
The Bolsheviks built the first socialist state after the October Revolution of 1917, and the People's Republic of China was declared in 1949 under Mao Zedong. At the turn of the 21st century China, Cuba, Laos, North Korea, and Vietnam remained the only officially Marxist-Leninist states, after most such states collapsed in the late 1980s and early 1990s.