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Society does not consist of individuals, but expresses the sum of interrelations, the relations within which these individuals stand. ~ Karl Marx

Marxism is a method of socio-economic inquiry based upon a materialist interpretation of historical development, a dialectical view of social change, and an analysis of class-relations and conflict within society and the role of class struggle in systemic economic change. Marxism is based on a materialist understanding of the development of society through the economic activities required by human society to provide for its material needs. The form of economic organization, or mode of production, is understood to be the (base) to every social phenomena including social relations, political and legal systems, morality and ideology (superstructure), this is known as Historical materialism or Dialectical materialism. The concept is based on Hegelian thesis-antithesis-synthesis dialectics.  By turning Hegel's idealist dialectics upside-down, Marx advanced his own theory of dialectical materialism, arguing that:

It is not the consciousness of men that determines their being, but, on the contrary, their social being that determines their consciousness.

This relationship between the superstructure and the base is reflexive; At first the base gives rise to the superstructure and remains the foundation of a form of social organization. Hence, that formed social organization can act again upon both parts of the base and superstructure, whose relationship is dialectic, namely a relationship driven by conflicts and contradictions.

The history of all hitherto existing society is the history of class struggles. Freeman and slave, patrician and plebeian, lord and serf, guild-master and journeyman, in a word, oppressor and oppressed, stood in constant opposition to one another, carried on uninterrupted, now hidden, now open fight, a fight that each time ended, either in a revolutionary reconstitution of society at large, or in the common ruin of the contending classes. ~ Engels

Marx investigates labor-power as a commodity. Labor-power existing on the market depends on two fulfillment's: the workers must offer it for temporary sale on the market and the workers must not possess the means to their own subsistence. As long as the labor-power is sold temporarily then the worker is not considered a slave. Worker dependence for a means of subsistence ensures a large working force, necessary for the production of capital. For the capitalist the worker possesses only one use-value, that of labor power. The capitalist buys from the worker his labor power, or his ability to do work, and in return the worker receives a wage, or a means of subsistence. The wage, is the first thing that Marx begins to re-explain in the opening of the chapter, stressing that it is equal to the quantity of the "necessaries of life habitually required by the average laborer". Under capitalism it is the capitalist who owns everything in the production process such as: the raw materials that the commodity is made of, the means of production, and the labor power (worker) itself. At the end of the labor process it is the capitalist who owns the product of their labor, not the workers who produced the commodities. Since the capitalist owns everything in the production process he is free to sell it for his own profit. The goal of the capitalist is to produce surplus value.

However, producing surplus value proves to be difficult. If all goods are purchased at their full price then profit cannot be made. Surplus value cannot arise from buying the inputs of production at a low price and then selling the commodity at a higher price. This is due to the economic law of one price which states "that if trade were free, then identical goods should sell for about the same price throughout the world". What this law means is that profit cannot be made simply through the purchase and sale of goods. Price changes on the open market will force other capitalists to adjust their prices in order to be more competitive, resulting in one price. Karl Marx points out that, "in its pure form, the exchange of commodities is an exchange of equivalents, and thus it is not a method of increasing value," and so a contradiction reveals itself. If the participating individuals exchanged equal values, neither of the individuals would increase capital. The needs being satisfied would be the only gain.

So, where does surplus value originate? Quite simply, the origin of surplus value arises from the worker. The following example is from Marx's Capital Volume I. A capitalist hires a worker to spin ten pounds of cotton into yarn. Suppose the value of the cotton is one dollar per pound. The entire value of the cotton is 10 dollars. The production process naturally causes wear and tear on the machinery that is used to help produce the yarn. Suppose this wearing down of machinery costs the capitalist two dollars. The value of labor power is three dollars per day. Now also suppose that the working day is six hours. In this example the production process yields up 15 dollars, and also costs the capitalist 15 dollars. Thus there is no profit. Now consider the process again, but this time the working day is 12 hours. In this case there is 20 dollars produced from the 20 pounds of cotton. Wear and tear on machinery now costs the capitalist four dollars. However, the value of labor power is still only three dollars per day. The entire production process costs the capitalist 27 dollars. However, the capitalist can now sell the yarn for 30 dollars. This is because the yarn still holds 12 hours of socially necessary labor time in it (equivalent to six dollars). The key to this is that workers exchange their labor power in return for a means of subsistence. In this example, the means of subsistence has not changed; therefore the wage is still only 3 dollars per day. Notice that while the labor only costs the capitalist 3 dollars, the labor power produces 12 hours worth of socially necessary labor time.

Labor power can produce more than its own value. In order for commodities to be produced with surplus value two things must be true. Man must be a living commodity, a commodity that produces labor power, and it must be the nature of this labor power to produce more than its own value. Marx says that surplus value is "merely a congealed quantity of surplus labor-time… nothing but objectified surplus labor". A Capitalist is always devising new ways to increase the surplus that he is receiving.

1. The first, or absolute, way the capitalist can increase surplus value is through extending the working day so the worker has more time to create value. Capitalism takes advantage of this extra time by paying the worker a wage that allows them to survive but is less than the value the same worker creates. So there are two parts to the working day. One part of the working day is the time necessary in order to produce the value of the workers labor power. The second part of the working day is surplus labor time, which produces no value for the laborer, but produces value for the capitalist. 
2. The second, or relative, way the capitalist can increase surplus value is to revolutionize changes in the production method. Marx describes the machine as the instrument of labor for the capitalists' material mode of existence. The machine competes with the worker, diminishing the use-value of the worker's labor-power. Marx also points out that with the advance in technology of machines led to the substitution of less skilled work for more skilled work which ultimately led to a change in wages. During the progression of machinery the numbers of skilled workers decreased, while child labor flourished, increasing profits for the capitalist.

Marx displays an example of surplus labor occurring in these favorable conditions in the case of the East Indies. The inhabitants would be able to produce enough to satisfy all of his needs with only twelve working hours per week. This provides for more than enough leisure time until capitalist production takes hold. Then he may be required to work six days per week to satisfy his needs—there can be no explanation of why it is necessary for him to provide the extra five days of surplus labor.

In pre-capitalist economies, exploitation of the worker was achieved via physical coercion. In the capitalist mode of production, because the worker does not own the means of production, he cannot survive except by working for capitalists. The reserve army of unemployed workers continually threatens employed workers, pushing them to work hard to produce for the capitalists with minumum wage while the capitalists get the highest profit. The worker's entry into such employment is voluntary in that he or she chooses which capitalist to work for. However, the worker must work or starve. Thus, exploitation is inevitable, and the "voluntary" nature of a worker participating in a capitalist society is illusory. The action of the law of supply and demand of labour on this basis completes the despotism of capital.

The capitalists argue that they have the right to extract all of the value from a day's labor, since that is what they bought. Similarly, the worker demands the full value of his own commodity. The worker needs to be able to renew his labor power so that it can be sold again anew. The capitalist sees working fewer hours as theft from capital, and the worker see working too many hours as theft from laborers. This class struggle can be seen throughout history, and eventually laws such as Factory Acts were put in place to limit the length of a working day and child labour.

So as we have seen, according to Marxist analysis, class conflict within capitalism arises due to intensifying contradictions between the minority (the bourgeoisie) who own the means of production, and the vast majority of the population (the proletariat) who produce goods and services. The bourgeoisie in the capital system get the surplus product in the form of surplus value (profit) due to exploitation of the proletariat. Specifically, the working class (proletariat) do not own capital and must live by selling their labour power in exchange for a wage. In capitalism, the labour theory of value is the operative concern; it states that the value of the product = the quantity of labor average  and productivity + capital of materials used. The profit or surplus-value arises when workers do more labor than is necessary to pay the cost of hiring their labor-power; thus, capitalist exploitation is realized as deriving surplus value from the worker.

As capitalism exploits and oppresses the proletariat, the contradiction becomes apparent to the proletariat, social unrest between the two antagonistic classes intensifies, culminating in a social revolution. The eventual long-term outcome of this revolution would be the establishment of socialism - a socioeconomic system based on cooperative ownership of the means of production,distribution based on one's contribution, and production organized directly for use. Karl Marx hypothesized that, as the productive forces and technology continued to advance, socialism would eventually give way to a communist stage of social development. Communism would be a classless, stateless, humane society based on common ownership and the principle of

"From each according to his ability, to each according to his needs".

Marx viewed religion as "the opium of the people" that had been used by the ruling classes to give the working classes false hope in an after life where they would be really rewarded while being exploited by the capitalists, while at the same time recognizing it as a form of protest by the working classes against their poor economic conditions.

After Marx

One of the first major political splits occurred in Marxism was when the social democrats argued that socialism should be achieved through evolution rather than revolution. Such views were strongly opposed by the revolutionary socialists, who argued that any attempt to reform capitalism was doomed to fail, because the reformists would be gradually corrupted and eventually turn into capitalists themselves.

Lenin and the Bolsheviks 

As he surveyed the European milieu in the late 1890s, Lenin found several theoretic problems with the Marxism of the late 19th century. Contrary to what Karl Marx had predicted,capitalism had become stronger in the last third of the 19th century. In Western Europe, the working class had become poorer, rather than becoming politically progressive, thinking people; hence, the workers and their trade unions, although they had continued to militate for better wages and working conditions, had failed to develop a revolutionary class consciousness, as predicted by Marx. To explain that undeveloped political awareness, Lenin said that the division of labour in a bourgeois capitalist society prevented the emergence of a proletarian class consciousness, because of the ten-to-twelve-hour workdays that the workers laboured in factories, and so had no time to learn and apply the philosophic complexities of Marxist theory. Lenin said that the “history of all countries bears out the fact that, through their own powers alone, the working class can develop only a trade-union consciousness”; and that under reformist, trade-union leadership, the working class could only engage spontaneous local rebellions to improve their political position within the capitalist system, and that revolutionary consciousness developed unevenly. Nonetheless, optimistic about the working class’s ability to develop a revolutionary class consciousness, Lenin said that the missing element for escalating the class struggle to revolution was a political organisation that could relate to the radicalism of political vanguard of the working class, who then would attract many workers from the middling policies of the reformist leaders of the trade unions.

The core ideological features of Marxism-Leninism are those of Marxism and Leninism, that is to say, belief in the necessity of a revolutionary overthrow of capitalism through communist revolution, to be followed by a dictatorship of the proletariat as the first stage of moving towards communism. The dictatorship of the proletariat refers to the absolute power of the working class like "paris commune". It is governed by a system of proletarian direct democracy, in which workers hold political power through local councils, known in the Russian Revolution as "soviets". Then arises the need for a vanguard party whose elections are democratic (centeral democracy) to lead the proletariat in this effort. Leninists argue that Lenin's ideal vanguard party would be one where membership is completely open, thus the organization would quickly include the entire working class and that all directing bodies of the Party, from top to bottom, shall be elected. The democratic aspect of this organizational method describes the freedom of members of the political party to discuss and debate matters of policy and direction, but once the decision of the party is made by majority vote, all members are expected to uphold that decision. This latter aspect represents the centralism. As Lenin described it, democratic centralism consisted of "freedom of discussion, unity of action."

The concept of a vanguard party was used by the Bolsheviks to justify their suppression of other parties. They took the line that since they were the vanguard of the proletariat, their right to rule could not be legitimately questioned. Hence, opposition parties could not be permitted to exist. The first goal of a Leninist party is to educate the proletariat, so as to remove the various modes of perceived false consciousness the bourgeois have instilled in them, instilled in order to make them more docile and easier to exploit economically, such as religion and nationalism.

Lenin advocated Marx's position of religion saying:

Religion is the opium of the people: this saying of Marx is the cornerstone of the entire ideology of Marxism about religion. All modern religions and churches, all and of every kind of religious organizations are always considered by Marxism as the organs of bourgeois reaction, used for the protection of the exploitation and the stupefaction of the working class.

But also expanded it to say:

Atheism is a natural and inseparable part of Marxism, of the theory and practice of scientific socialism 

The Mensheviks 

The Mensheviks were more inclined to work with the liberal "bourgeois" democratic parties such as the Constitutional Democrats, because these would be the "natural" leaders of a bourgeois revolution. In contrast, the Bolsheviks didn't believe that the Constitutional Democrats were capable of sufficiently radical struggle and tended to advocate alliances with peasant representatives and other radical socialist parties such as the Socialist Revolutionaries. In the event of a revolution, this was meant to lead to a dictatorship of the proletariat, which would carry the revolution to the end. The Mensheviks came to argue for predominantly legal methods and trade union work, while the Bolsheviks favoured armed violence. Some Mensheviks left the party after 1905 and joined legal opposition organisations. After a while, Lenin's patience wore out with their compromising and in 1908 he called these Mensheviks "liquidationists".

Trotsky

Lenin consistently explained "this elementary truth of Marxism, that the victory of socialism requires the joint efforts of workers in a number of advanced countries". Modern followers of Leon Trotsky maintain that as predicted by Lenin, Trotsky advocated proletarian revolution as set out in his theory of "permanent revolution", and he argued that in countries where the bourgeois-democratic revolution had not triumphed already (in other words, in places that had not yet implemented a capitalist democracy, such as Russia before 1917), it was necessary that the proletariat make it permanent by carrying out the tasks of the social revolution at the same time, in an uninterrupted process. Trotsky believed that a new socialist state would not be able to hold out against the pressures of a hostile capitalist world unless socialist revolutions quickly took hold in other countries as well, especially in the industrial powers with a developed proletariat.

Stalin

"Socialism in One Country" was a theory put forth by Joseph Stalin in 1924, elaborated by Nikolai Bukharin in 1925 and finally adopted by Stalin as state policy. The theory held that given the defeat of all the communist revolutions in Europe in 1917–1921 except Russia's, theS oviet Union should begin to strengthen itself internally. That was a shift from the previously held Marxist position that socialism must be established globally. But the USSR ceased to show the characteristics of a socialist state long before its formal dissolution. The USSR had developed new class structures: those who are in government and therefore have power (sometimes referred to as the political class), and those who are not in government and do not have power, the working class. This is taken to be a different form of capitalism, in which the government, as owner of the means of production, takes on the role formerly played by the capitalist class; this arrangement is referred to as "state capitalism". Some academics such as Chomsky dispute the claim that the political movements in the former Soviet Union were Marxist.

Communist governments have historically been characterized by state ownership of productive resources in a centrally planned economy and sweeping campaigns of economic restructuring such as nationalization of industry and land reform (often focusing on collective farming or state farms.) While they promote collective ownership of the means of production, Communist governments have been characterized by a totaliterian state apparatus in which decisions are made by the ruling Communist Party.

Mao

Unlike the earlier forms of Marxism-Leninism in which the urban proletariat was seen as the main source of revolution, and the countryside was largely ignored, Mao believed that peasantry could be the main force behind a revolution, led by the proletariat and a vanguard Communist party. The model for this was the Chinese communist rural Protracted People's War of the 1920s and 1930s, which eventually brought the Communist Party of China to power. Furthermore, unlike other forms of Marxism-Leninism in which large-scale industrial development was seen as a positive force, Maoism made all-round rural development the priority. Mao felt that this strategy made sense during the early stages of socialism in a country in which most of the people were peasants. Unlike most other political ideologies, including other socialist and Marxist ones, Maoism contains an integral military doctrine and explicitly connects its political ideology with military strategy. In Maoist thought, "political power grows from the barrel of the gun" (a famous quote by Mao), and the peasantry can be mobilized to undertake a "people's war" of armed struggle involving guerrilla warfare.