Karl Marx: 1818-1883. German philosopher, economist and radical reformer. Writer of several books, of which The Communist Manifesto (with Friedrich Engels) and Capital became best known.
The fate of Karl Marx is curious: During his life he was hardly known, poor and obscure, but his writings inspired modern socialism and communism, and the founders of the Soviet-Union (Lenin, Trotsky, Stalin) and of Communist China (Mao), and thus his philosophy influenced the lives, health and happiness of literally billions of men, women and children, and indirectly caused the deaths of many millions.
It is difficult or impossible to reduce the acts and decisions of dictators to the writings of those in whose name they claim to act, and it seems rather probable that Marx would not at all have approved of Stalin or Mao, possibly in a similar sense in which Jesus would have rejected all similarity between his teachings and the practices of the Borgia-pope, the Inquisition or the Jesuits, but it is also true that if Marx had not written his philosophy and economy these dictators would not have had a ready-made theory to ease their ways to power and to use as a basis for their policies and their ideologies. (If you don't know it: The Soviet-Russian icons with the barber-advertisement - Marx, Engels, Lenin, Stalin with progressively less facial hair - are interesting, as icons.)
A. Marx' works and theories
Marx own writings are rather obscure, though The Communist Manifesto is a well-written pamphlet - which may have a lot to do with Engels, with whom Marx cooperated, and who wrote a more readable prose than Marx did. The Marxian writings are also quite voluminous, and not interesting - unless, of course, you are a true Marxist believer with very little to do.
The main Marxian teachings may be and have been isolated as follows:
1. Historical materialism: The notion that human history is made by and based on class struggle - the fight between the exploited masses and their exploiters of various kinds, whether slave-holders, feudal barons, or capitalist entrepreneurs.
As an intellectual proposition, this can hardly be taken serious, though it has been, but as a basis for propaganda among the working classes it is of course most helpful. It is effectively and rhetorically stated by The Communist Manifesto.
It cannot be taken serious, because it reduces an extra-ordinarily complicated and multi-facetted process to one single cause, and at the same time excludes all sorts of features, facts and events that do have an influence in human history, such as fashions in political and religious ideas, changes in the weather, technological inventions or scientific ideas from having any influence at all on the course of history. Also, it takes a lot of faith to believe in classes struggling like organisms - and in fact the notion of class struggle seems a typical category mistake, in that it attributes characteristics of individuals to collections of individuals. Individuals may struggle, groups may struggle, but classes not, just as classes may be numerous, but individuals not.
2. Dialectical materialism: The notion that all of reality is material in movement, and propelled by internal contradictions.
This can be taken even less serious than historical materialism, though again it has been taken serious by many. Marx took it from Hegel, who was an idealist, who in turn based his dialectics on how people argue (by thesis, anti-thesis and synthesis, or so Hegel claimed). It is manifestly contradictory, but precisely for that reason an effective instrument in discussions: When a Marxist contradicts himself or when his theory seems to be contradicted by the facts, all he needs to do is to smile contemptuously and praise the dialectics of reality.
But again, as with historical materialism, the notion seems a category mistake: Arguments may be contradictory, but not real things, or only metaphorically, for what is contradictory thereby cannot exist.
3. Labor and surplus theory of value: The notion that the value of a commodity is proportional (equal) to the quantity of human labor necessary to produce it coupled to the notion that the worker receives from the capitalist only a part of the value of the commodities the laborer makes.
The labor theory of value was originated by Adam Smith, or perhaps even by Aristotle in the Ethics, and developed by David Ricardo. It is difficult to combine with market conditions, where the prices of commodities depend on demand much rather than on the cost of producing them, but something can be said in its favor in mathematical economics. (See: Sraffa: 'Producing commodities by means of commodities')
Marx' surplus value theory simply is an explanation for profit that amounts to the claim: 'Profits is what gets stolen from the workers by the capitalists'. It is quite unrealistic, though good propaganda, and what is reasonable in it could be expressed as the moral proposition: 'Profits made by firms ought to be fairly divided between those who work in or for the firms'.
Marx has often been presented as if he were a great philosopher or a great economist, but he was neither the one nor the other. He was a political radical who was intelligent enough to work out a philosophy and economics to underpin his radicalism, but he got (in)famous only because his kind of radicalism - socialism, communism, social democracy - got popular and powerful in the last quarter of the 19th and first half of the 20th Century, and because he was made the ideologist of those movements.
Also, it should be noted that Marx was not the originator of communism or communist ideals. These may be as old as mankind, and in Marx' case there is a considerable influence of Babeuf, a communist who perished during the French Revolution.
B. Marx the person
As a person, Marx seems to have been not sympathetic. He quarrelled easily and a lot; was overbearing, arrogant, and self-willed; and did not treat his wife and children very well. In excuse, it may be said that he had a difficult life and worked hard to write his books, that were not well-received while he lived, and that he had the courage of his convictions, while it is also true that in his time the members of the working class were mercilessly exploited.
There are quite a lot of biographies of him, of which the earlier ones and the Soviet ones tend to be hagiographies.