I’m not a Muslim. But I’m curious as to what Muslims believe is the answer to this question. Do all Muslims agree on one definition? What do you think? Who is God?
Yes, the God has been described well in Qur'an. But the descriptions are not like mathematical proofs but are philosophical and infrastructural; Here are the examples from Qur'an:
He says: [Shaykh al-Saduq, al-Tohid, page ~480]
Hope these help :)
Sūrat al-Ikhlāṣ provides a good insight about how Muslims view Allah:
Also, the 99 Names of Allah are another source of His attributes. They are far too many to list here, but this Wikipedia article does a good job of listing them with English translations: http://en.wikipedia.org/wiki/99_Names_of_God
Here, the consensus ends. Some Shi'a scholars believe that Allah has no physical form and cannot be seen (by the eye). Among Sufis there is a belief that the whole universe is a manifestation of Allah. Some Sunnis, on the other hand, believe that Allah does have a physical presence that is vaguely human (with hands and feet). Many others (from all sects) believe that this is an unanswerable question.
Talking from a Shia perspective, @YasserZamani and @Ahmadi have answered the question very good, and from the other answers you can easily see that not all the Muslims agree on one understanding of Allah. However, let me put the issue differently so that you can hopefully find more coherence behind all of them.
All those who believe in a Heavenly religion, Muslims, Christians and Jews, as far as I know define God as a perfect being. This very beginning is the same in all such perspectives. However, the interpretation of being perfect is somewhat different and this is understandable from the distinctions between teachings of different schools and religions.
For example, God is considered as omnipresent and omnipotent in all such schools and religions but then see how differently would they use these reputations to talk about their God, which is of course a same God for all of them (differeny understanding of a same notion):
So you see, from the very fundamental levels of teachings of the prophets and their successors --peace be upon them all-- all of us, Shia or Sunni, Muslim or Christian or Jew, think the same, God is perfect, but then some have their own interpretations of those teachings and one should personally seek for the one interpretation which appear as rigorous and reasonable:
In Islam, God is the creator of the Universe. He is the the most powerful being, the most most beneficent, the most merciful. There are in infact 99 names for God in Islam. All these names depict a quality in God. In other words, they are praise worth names of God.
There is no conflict among the definition of God in Islam, what so ever. In fact there is one chapter in Quran about who is God, named Tashid. The translation is
In Chapter Yasin, the power of God is depicted as
This basically means, when he wishes to do something, it happens automatically.
Also the main crux of Islam is to recognize God and say that he is the only God and there is no one beside him who is worthy of worship.
The second clause in Islam is to recognize Prophet Muhammad who was the true prophet of God through him we know God.