Arguments for the oneness of God
Theologians usually use reason and deduction to prove the existence, unity and oneness of God. They use a teleological argument for the existence of God as a creator based on perceived evidence of order, purpose, design, or direction-or some combination of these-in nature. Teleology is the supposition that there is a purpose or directive principle in the works and processes of nature.
Another argument which is used frequently by theologians is Reductio ad absurdum. They use it instead of positive arguments as a more efficient way to reject the ideas of opponents. The Quran has also been used this way in several cases.
God as the cause of causes
Main article: Kalam cosmological argument
Against the polytheism of pre-Islamic Arabia, the Qur'an argues that the knowledge of God as the creator of everything rules out the possibility of lesser gods since these beings must be themselves created. For the Qur'an, God is an immanent and transcendent deity who actively creates, maintains and destroys the universe. The reality of God as the ultimate cause of things is the belief that God is veiled from human understanding because of the secondary causes and contingent realities of things in the world. Thus the belief in the oneness of God is equated in the Qur'an with the "belief in the unseen" (Sura 2:3). The Qur'an summarizes its task in making this "unseen", to a greater or lesser degree "seen" so that belief in the existence of God becomes a Master-Truth rather than an unreasonable belief. The Qur'an states that God's signals are so near and yet so far, demanding that its students listen to what it has to say with humility (Sura 50:33, Sura 50:37). The Qur'an aims to draw attention to certain obvious facts, turning them into "reminders" of God instead of providing lengthy "theological" proofs for the existence and unity of God.
Ash'ari theologians rejected cause and effect in essence, but accepted it as something that facilitates humankind's investigation and comprehension of natural processes. These medieval scholars argued that nature was composed of uniform atoms that were "re-created" at every instant by God. The laws of nature were only the customary sequence of apparent causes (customs of God), the ultimate cause of each accident being God himself.
God as the necessary existent
See also: Cosmological argument and ontological argument
An ontological argument for the existence of God was first proposed by Avicenna (965-1037) in the Metaphysics section of The Book of Healing which is known as Contingency and necessity argument (Imakan wa Wujub).
Avicenna initiated a full-fledged inquiry into the question of being, in which he distinguished between essence (Mahiat) and existence (Wujud). He argued that the fact of existence can not be inferred from or accounted for by the essence of existing things and that form and matter by themselves cannot interact and originate the movement of the universe or the progressive actualization of existing things. Existence must, therefore, be due to an agent-cause that necessitates, imparts, gives, or adds existence to an essence. To do so, the cause must be an existing thing and coexist with its effect.
This was the first attempt at using the method of a priori proof, which utilizes intuition and reason alone. Avicenna's proof of God's existence is unique in that it can be classified as both a cosmological argument and an ontological argument. "It is ontological insofar as ‘necessary existence' in intellect is the first basis for arguing for a Necessary Existent". The proof is also "cosmological insofar as most of it is taken up with arguing that contingent existents cannot stand alone and must end up in a Necessary Existent."  Another argument Avicenna presented for God's existence was the problem of the mind-body dichotomy.
According to Avicenna, the universe consists of a chain of actual beings, each giving existence to the one below it and responsible for the existence of the rest of the chain below. Because an actual infinite is deemed impossible by Avicenna, this chain as a whole must terminate in a being that is wholly simple and one, whose essence is its very existence, and therefore is self-sufficient and not in need of something else to give it existence. Because its existence is not contingent on or necessitated by something else but is necessary and eternal in itself, it satisfies the condition of being the necessitating cause of the entire chain that constitutes the eternal world of contingent existing things. Thus his ontological system rests on the conception of God as the Wajib al-Wujud (necessary existent). There is a gradual multiplication of beings through a timeless emanation from God as a result of his self-knowledge.
Indivisibility of God's sovereignty
The Qur'an argues that there can be no multiple sources of divine sovereignty since "behold, each god would have taken away what [each] had created, And some would have Lorded it over others!" The Qur'an argues that the stability and order prevailing throughout the universe shows that it was created and is being administered by only one God (Sura 28:70-72). Verses 27:60-64 for example read:
"Who has created the heavens and the earth, and Who sends you down rain from the sky? Yea, with it We cause to grow well-planted orchards full of beauty of delight: it is not in your power to cause the growth of the trees in them. (Can there be another) god besides Allah? Nay, they are a people who swerve from justice.Or, Who has made the earth firm to live in; made rivers in its midst; set thereon mountains immovable; and made a separating bar between the two bodies of flowing water? (can there be another) god besides Allah? Nay, most of them know not. Or, Who listens to the (soul) distressed when it calls on Him, and Who relieves its suffering, and makes you (mankind) inheritors of the earth? (Can there be another) god besides Allah? Little it is that ye heed! Or, Who guides you through the depths of darkness on land and sea, and Who sends the winds as heralds of glad tidings, going before His Mercy? (Can there be another) god besides Allah?- High is Allah above what they associate with Him! Or, Who originates creation, then repeats it, and who gives you sustenance from heaven and earth? (Can there be another) god besides Allah? Say, "Bring forth your argument, if ye are telling the truth!"
- Qur'an, Sura 27 (Al-Naml), ayat 60-64
The Qur'an in verse 21:22 states: "If there were numerous gods instead of one, [the heavens and the earth] would be in a sorry state". Later Muslim theologians elaborated on this verse saying that the existence of at least two gods would inevitably arise between them, at one time or another, a conflict of wills. Since two contrary wills could not possibly be realized at the same time, one of them must admit himself powerless in that particular instance. On the other hand, a powerless being can not by definition be a god. Therefore the possibility of having more than one god is ruled out.
The Qur'an argues that human beings have an instinctive distaste for polytheism: At times of crisis, for example, even the idolaters forget the false deities and call upon the one true God for help. As soon as they are relieved from the danger, they however start associating other beings with God. "So when they ride in the ships they call upon Allah, being sincerely obedient to Him, but when He brings them safe to the land, lo! they associate others (with Him)" (Sura 29:65).
Next, the Qur'an argues that polytheism takes away from human dignity: God has honored human beings and given them charge of the physical world, and yet they disgrace their position in the world by worshipping what they carve out with their own hands.
Lastly, the Qur'an argues that monotheism is not a later discovery made by the human race, but rather there is the combined evidence of the prophetic call for monotheism throughout human history starting from Adam. The Qur'an suggests several causes for deviation from monotheism to polytheism: Great temporal power, regarded by the holder and his subjects as 'absolute' - may lead the holder to think that he is God-like; such claims were commonly forced upon, and accepted by, those who were subject to the ruler. Also, certain natural phenomena (such as the sun, the moon and the stars) inspire feelings of awe, wonder or admiration that could lead some to regard these celestial bodies as deities. Another reason for deviation from monotheism is when one becomes a slave to his or her base desires and passions. In seeking to always satisfy the desires, he or she may commit a kind of polytheism.