Inductive
If the premises of the argument are true then the conclusion is likely
A posteriori
Based on evidence and experience
Summa Theologica
Work written by Aquinas which includes cosmological argument
Change/Motion
When we observe the universe, we notice that things do not move of their own accord, rather they are moved by something else. If we look back on a set of movements, eventually we would find something external that started the chain of change or movement. Aquinas argued that there must be an 'unmoved mover', not itself being moved or changed by anything else, by the mover of all other things. For Aquinas, this unmoved mover is God.
Cause
Aquinas argued that it is impossible to have an infinite chain of causes, and so again by reductio ad absurdum, there must be first cause. According to Aquinas, this cause must be external to the outside universe as nothing can cause itself. God himself is the external first cause, who is outside of time and not caused into existence, yet causes everything else into existence.
Contingency
Aquinas argued that everything that exists, has the possibility to not exist. Following this, in order for things to exist, there has to be a non-contingent being that brought everything else into existence. This being must be unlike anything else in existence and can have no beginning or end in order to be non-contingent - and for Aquinas, this is God