Communism is a theory for revolutionary change and political and socioeconomic organization based on common control of the means of production as opposed to private ownership.
In Marxist Theory, communism is a specific stage of historical development that inevitably emerges from the development of worldwide socialism that leads to a superabundance of material wealth, allowing for distribution based on need and social relations based on freely-associated individuals.
The communist idealogy was expressed by Karl Marx in his 1848 Communist Manifesto. The book expressed concerns of the working citizens, such as the working man's subjection to capital (meaning, the worker's being forced to work by the standards of the time).
Communist Manifesto often references to the proletariat as the working class and the Bourgeois as a social class "characterized by their ownership of capital and their related culture". 
The Soviet Union 1924-1991
The Russian Revolution in 1917, led by Vladimir Lenin, resulted in the formation of the first communist state, the Soviet Union. The revolution was a culmination of unrest and social repression in Russia under the tsars.
The Soviet Union was a federal socialist republic led by the communist party, until the Stalinist degeneration. It's military, the Red Army was the leading factor of the Allies victory in World War II, and the threat to the Americans during the Cold War. 
Karl Marx, in his 1848 Communist Manifesto, founded the basis of Marxist Theory.
Marxism is the system of economic and political thought developed by Karl Marx, along with Friedrich Engels, especially the doctrine that the state throughout history has been a device for the exploitation of the masses by a dominant class, that class struggle has been the main agency of historical change, and that the capitalist system, containing from the first the seeds of its own decay, will inevitably, after the period of the dictatorship of the proletariat, be superseded by a socialist order and a classless society. 
Being the first principle behind communism, Marxism is often considered true communism.
Lenin accepted most of Marx's thought without alteration. He prided himself upon his Marxist orthodoxy, attacking any new idea that struck him as heretical. But probably his greatest hatred was reserved for the so-called Revisionism of Bernstein and other avant-garde socialist intellectuals who admitted, among other things, that contrary to Marx the absolute living standard of workers had vastly improved under capitalism.
But if the intellectuals guide the workers, who guides the intellectuals? That, Lenin answered, is to be done by a rigidly hierarchical, strictly disciplined Party - headed by himself. As Lenin continued to develop his tactical views, it became clear that not only would the party lead the proletariat to victory, but would also hold the reins of power for the proletariat after victory was achieved. Leon Trotsky, though initially a critic of Lenin, eventually became his enthusiastic supporter; he explained their doctrine thusly: In the composition of [the proletariat] there enter various elements, heterogeneous moods, different levels of development. Yet the dictatorship pre-supposes unity of will, unity of direction, unity of action. By what other path can it be attained? The revolutionary supremacy of the proletariat presupposes within the proletariat itself the political supremacy of a party, with a clear program of action and a faultless internal discipline.
Lenin conspicuously failed to elaborate upon the great void in Marxist theory: to wit, precisely what would "socialism" be? Marx had repeatedly declared it "unscientific" to specify - a clever trick for uniting quarreling socialists, but hardly intellectually satisfying. Lenin scarcely advanced further than this when he seized power: "All citizens are here transformed into hired employees of the state, which is made up of the armed workers... All that is required is that they should work equally, should regularly do their share of the work, and should receive equal pay. The accounting and control necessary for this have been simplified by capitalism to the utmost, till they have become the extraordinarily simple operations of watching, recording and issuing receipts, within the reach of anybody who can read and write and knows the first four rules of arithmetic." But Lenin combined simple-minded programs with a calculating cynicism. For whatever policies he might advocate, there was but one target in his sights, as he plainly states: "The point of the uprising is the seizure of power; afterwards we will see what we can do with it." 
Maoism is the ideology and methodology for revolution developed by Mao Zedong and his associates in the Chinese Communist Party from the 1920s until Mao’s death in 1976. Maoism has clearly represented a revolutionary method based on a distinct revolutionary outlook not necessarily dependent on a Chinese or Marxist-Leninist context.