The Islamic doctrine of God is tawhid, the assertion of an absolute and undivided oneness, and it is stated most compactly in Surat al-Ikhlas, the hundred and twelfth chapter of the Qur'an, four short verses in constant recitation: "Say: He is God, One; God, the Eternally Sufficient; He begets not, nor was He begotten; and there is none comparable unto Him." Qur'an 42:11 puts the denial of likeness in a single clause: "there is nothing like unto Him." Both cut against any account of God that admits generation, division or resemblance to anything created.
The corresponding sin is shirk, association, setting up any partner, equal or intermediary alongside God. The Qur'an names it the one sin that is not forgiven in a person who dies in it (4:48), and it is the frame in which the Qur'an addresses Christian claims. 4:171 tells the People of the Book not to exceed the bounds of their religion and to "say not: Three"; 5:73 says that those who call God "the third of three" have disbelieved; 5:116 stages a scene at the judgement in which Jesus is asked whether he told people to take him and his mother as gods besides God. Read plainly, this is a direct theological contradiction of Trinitarianism, and the atlas does not soften it.
How far those verses reach is itself argued within Islamic scholarship, and the argument matters for the next section. Classical commentators including Ibn Kathir read them as refuting the doctrine of the Trinity as such. The Study Quran, edited by Seyyed Hossein Nasr, argues the contrary: that orthodox Trinitarian theology does not make God one of three, and that the verses address a tritheism, and a divinising of Mary, which mainstream Christianity itself rejects. Both readings are held by serious Muslim scholars, and the question will not be settled by quotation.
God is known through the ninety-nine names, al-asma al-husna, the most beautiful names: al-Rahman the Merciful, al-Rahim the Compassionate, al-Malik the Sovereign, al-Quddus the Holy. The first two open all but one chapter of the Qur'an. What the names actually predicate of God occupied kalam, Islamic speculative theology, for centuries. The Mu'tazila held that affirming eternal attributes distinct from the divine essence compromised the oneness it was meant to protect; the Ash'aris affirmed the attributes and refused to specify their manner, bila kayf, "without asking how". The position that hardened into Sunni orthodoxy is closer to the second.