The ways of demonstrating the existence of God formulated by Aquinas (Summa Theologiae, Ia 3: it is important in understanding the significance of these arguments to Aquinas that the entire context stretches from Ia 2 to 11). They are:
All the arguments are physico-theological arguments. The second is a first cause argument, and the first is the Aristotelian variety of it (accepted by Averroës) that singles out the causes of motion as particularly in need of a starting-point (
see mover, unmoved). The third is a variety of the cosmological argument, as it had been formulated by Avicenna (but rejected by Averroës). The fourth is the degrees of perfection argument. The fifth is a version of the argument from (or to) design.
http://www.aquinasonline.com/Topics/5ways.html A list of internet resources on the Five Ways
http://www.newadvent.org/summa/1002.htm Translated extracts on the Five Ways from the Summa Theologiae