One of the best and most simple proofs for the unity of God is the proof of ‘infinite being’ suggested by the Muslim philosopher Mulla Sadra.
P1. God is necessarily infinite.
P2. There is no plurality in an infinite being.
C: Therefore there is no possible plurality in Godhead.
Various Ayaat in the Quran prove the unity of God. For instance, see chapters 6:12-17, 21:22, 23:91, 28:88 and chapter 112.
In explaining the Unity of God, Imam Ali (as) says: “When someone says God is One, it could have four different meanings; two of which are wrong and the other two are correct. If you say: God is one in its numerical sense, then this is wrong, for, there is no second or third for God. Thus, those who said: “He is the third of the three” are blasphemous. Similarly, if one says: “He is one of the people” it is wrong for he has likened God to his creation. Glory be to Allah. The other two correct meanings of the oneness of God is either to say: He is One meaning there is none like unto Him” or to say: “He is One in that He has no divisions whether in external existence or in our mind. Such is our exalted Lord.”