The largest issue that thomas aquinas attempts to prove in his summa theologica is the existence of

God

Explanation:

In his Summa Theologiae Ia 2.3, Aquinas provides five proofs for the existence of God, famously known as the five ways. He distinguishes different perceptible events and then ventures to prove that their cause is none other than God. The events Aquinas mentions are motion, the existence of efficient causes,  the reality of contingency, the different grades of perfection in the natural order, and the end-directed activity of natural objects.