You need to be able to outline the first 3 of the 'five ways' that Aquinas uses to 'prove' God's existence.

Aquinas' Cosmological Argument

Aquinas bases his cosmological argument on the first three ways of his "Quinquae Viae", which are referred to as:

1) motion;

2) efficient causation;

3) contingency.

The First Way: Motion

Aquinas defines motion as: "motion is going from potential to actual", and suggests that there must be an "Unmoved Mover".

The Second Way: Efficient Causation

More commonly known as 'causation', this way suggests that there has to be an "Uncaused First Cause". This way was also influenced by Aristotle.

The Third Way: Contingency

This way is taken from possibility and necessity, and recognises how objects we see day to day are in fact contingent. This way suggests that there must be a 'Necessary Being'.

In all of these ways, Aquinas comes to the conclusion that the 'Unmoved Mover", "Uncaused First Cause" and "Necessary Being" is in fact God.

The cosmological argument has also been presented by other philosophers. The 'kalam' version has recently been revived by William Craig. Aquinas' contingency argument was famously supported by Father Copleston in a radio debate with Bertrand Russell. 

There are many Criticisms of the Cosmological Argument, as the logic has been attacked by philosophers such as Hume, Russell, and scientists such as Richard Dawkins.