Causality is a way to describe how different events relate to one another. Suppose there are two events A and B. If B happens because A happened, then people say that A is the cause of B, or that B is the effect of A.

What looks very simple, is in fact a difficult problem. Many people have tried to solve it, they have come up with different solutions

Causality in Philosophy

Aristotle 

Aristotle was a Greek philosopher. He also looked at the problem of causality. In his books Posterior analytics and Metaphysics he wrote:
 "All causes are beginnings..."
 "... we have scientific knowledge when we know the cause..."
 "... to know a thing's nature is to know the reason why it is..."
This can be used to explain causality. Aristotle found different kinds of causes:

 The material cause is that "raw material" from which a thing is made.  This is sometimes called  the part-whole causation. Example: The bronze of a statue.
 The formal cause tells us what, by using the example of an artist, a thing is planned to be.  This is sometimes called the whole-part causation. Example the shape of a statue.
 The efficient cause is that external thing that causes the change in the first place. It shows ' what causes change of what is changed'. It covers all possible types of things, and is the modern definition of cause.  Example: the artisan making the statue, the art of bronze-working, the man who gives the advice, the father of a child.
 The final cause describes why something exists.  The final cause, or telos, is the purpose of the thing.  This includes modern ideas of causation, such as wanting or needing something to be, or those that give a purpose to behaviour  Example: The reason why the artist wanted to make the statue.

Aristotle told people of two types of causes: proper (prior) causes and accidental (chance) causes. Both types of causes, can be spoken as potential or as actual, particular or generic. The same language refers to the effects of causes; so that generic effects assigned to generic causes, particular effects to particular causes, and operating causes to actual effects. It is also essential that ontological causality does not suggest the temporal relation of before and after - between the cause and the effect; that spontaneity (in nature) and chance (in the sphere of moral actions) are among the causes of effects belonging to the efficient causation, and that no incidental, spontaneous, or chance cause can be prior to a proper, real, or underlying cause per se.

All investigations of causality coming later in history will consist in imposing a favorite hierarchy on the order (priority) of causes; such as "final > efficient > material > formal" (Aquinas), or in restricting all causality to the material and efficient causes or, to the efficient causality (deterministic or chance), or just to regular sequences and correlations of natural phenomena (the natural sciences describing how things happen rather than asking why they happen).

David Hume 
David Hume was another philosopher who looked at the relation between cause and effect. Hume thinks that there are certain things all such relations of cause and effect have in common.:
 Cause and effect must be located close to each other. It is possible that causes far away have an effect close by, but they can only do this by a chain of cause-effect reactions.
 The effect always comes after the cause.
 There is a third element, called force or necessity. Water is usually fluid and transparent. From these properties, it is not apparent however that a man can suffocate in it.

Hume says that if someone is used to always seeing the same things occur in the same order, he will get accustumed to them being in that order. When he sees one event occur, he will expect the other to occur as well:

Causality in Logic 
Logic is the science that looks at how to build an argument. In Logic, there are usually two different types of causes. They are called necessary cause and sufficient cause.
 A necessary cause is a cause that says: Whenever B occurs, A will also have occurred. Knowing that A occurred, on the other hand does not necessarily imply that B will also have occurred.  Example: Senators in the United States need to be at least 30 years old. People that are younger cannot become senators. Therefore, any senator is at least 30 years old. (On the other hand: there are people that are at least 30 years old  that are not senators).
 A sufficient cause is a cause that says If I know A occurred, I can conclude that B also occurred. Example:  The center of a playing card is marked with a special symbol, called a large spade (♠). This is sufficient to say that the card is an ace.  There are three other cards in the game that are also aces. They are marked with a diamond (♦), a heart (♥), or a club (♣). It is not necessary to know that these three other cards exist or what they mean. On the other hand, there are no cards that are aces, except for those listed.

Related pages 
Free will
Determinism
Karma

References

Other websites 
 "The Art and Science of Cause and Effect": a slide show and tutorial lecture by Judea Pearl
 "The Buddhist Dharma of Cause and Effect as seen in the Lotus Sutra" : a Buddhist school based on this law of life as seen in the Lotus Sutra. Website in Italian and English.

Stanford Encyclopedia of Philosophy 
 Aristotle on Causality
 Kant and Hume on Causality
 Backwards Causation
 Probabilistic Causation
 Causation and Manipulability
 Counterfactual Theories of Causation
 Causal Processes
 Causation in the Law
 Medieval Theories of Causation
 The Metaphysics of Causation

General 
 Dictionary of the History of Ideas:  Causation
 Dictionary of the History of Ideas:  Causation in Law
 Dictionary of the History of Ideas:  Causation in History

Logic