The concept of God (Allah) in Islam is enunciated by God Himself in His revelation, the Holy Qur'an. It is expanded upon by the Final Prophet of God, Muhammad [peace upon him and his household] and further clarified by the successor to the Prophet, the Imam Ali.
The Holy Qur'an
Say: He, Allah, is One.
Allah is He on Whom all depend.
He begets not, nor is He begotten.
And none is like Him.
[Source: The Holy Qur'an, translated by M. H. Shakir, Chapter 112, verses 1-4]
Muhammad [pbuh], the Prophet of Islam
"Praise belongs to God, who in His firstness was solitary and in His beginninglessness was tremendously exalted through divinity and supremely great through His magnificence and power. He originated that which He produced and brought into being that which He created without a model preceding anything that He created. Our Lord, the eternal, unstitched (the heavens and the earth) through the subtlety of His lordship and the knowledge within His omniscience, created all that He created through the laws of His power, and split (the sky) through the light of dawn. So none changes His creation, none alters His handiwork, 'none repels His law' (XIII, 45) , none rejects His command. There is no place of rest away from His call, no cessation to His dominion and no interruption of His term. He is the truly existent from the first and the truly enduring forever. He is veiled from His creatures by His light in the high horizon, in the towering might, and in the lofty dominion. He is above all things and below all things. So He manifested Himself to His creation without being seen, and He transcends being gazed upon. He wanted to be distinguished by the profession of Unity when He withdrew behind the veil of His light, rose high in His exaltation and concealed Himself from His creation.
"He sent to them messengers so they might be His conclusive argument against His creatures and so His messengers to them might be witnesses against them. He sent among them prophets bearing good tidings and warning, 'that whosoever perished might perish by a clear sign, and by a clear sign he might live who lived' (VIII, 42) and that the servants might understand of their Lord that of which they had been ignorant, recognise Him in His Lordship after they had denied (it) and profess His Unity in His divinity after they had stubbornly resisted."
[Source: Muhammad Baqir Majlisi, Bihar al-Anwar, vol. 4, pp. 287-8]
Ali [as], the first Imam, successor to the Prophet
"He is distinct in attributes from all that He has originated, inaccessable to perception because of the changing essences He has created (in things), and outside of all domination by changing states because of grandeur and tremendousness. Forbidden is His delimitation to the penetrating acumen of sagacities, His description to the piercing profundities of thought and His representation to the searching probes of insight.
"Because of His tremendousness places encompass Him not, because of His majesty measures gauge Him not, and because of His grandeur standards judge Him not. Impossible is it for imaginations to fathom Him, understandings to comprehend Him or minds to imagine Him. Powers of reason with lofty aspiration despair of contriving to comprehend Him, oceans of knowledge run dry without alluding to Him in depth , and the subtleties of disputants fall from loftiness to pettiness in describing His power.
"He is One, not in terms of number; Everlasting, without duration; Standing, without supports. He is not of a kind that other kinds should be on a par with Him, nor an object that objects should be similar to Him, nor
like things that attributes should apply to Him. Powers of reason go astray in the waves of the current of perceiving Him, imaginations are bewildered at encompassing the mention of His beginninglessness, understandings are held back from becoming conscious of the description of His power, and minds are drowned in the depths of the heavens of His kingdom.
"He is Master over (giving) bounties, Inaccessable through Grandeur, and Sovereign over all things. Time makes Him not old, nor does description encompass Him. Humbled before Him are the firmest of obduracies in the limits of their constancy, and submitted to Him are the most unshakeable of the cords in the extremity of their towering regions .
"Witness to His Lordship is the totality of kinds, to His Power their incapacity, to His eternity their createdness, and to His permanence their passing into extinction. So they possess no place of refuge from His grasp of them, no exit from His encompassing them, no way of veiling themselves from His enumeration of them and no way of avoiding His power over them. Sufficient is the perfection of His making them as a sign, His compounding of their (natural) constitutions as a proof, the temporal origin of their natures as (a reason for His) eternity, and the creation's laws governing them as a lesson . No limit is attributed to Him, no similitude struck for Him and nothing veiled from Him. High indeed is He exalted above the striking of similitudes and above created attributes!
"And I testify that there is no god but He, having faith in His Lordship and opposing whoso denies Him; and I testify that Muhammad (PBUH) is His servant and messenger, residing in the best lodging-place, having passed from the noblest of loins and immaculate wombs, extracted in lineage from the noblest of mines and in origin from the most excellent of plantations, and (derived) from the most inaccessible of summits and the most glorious roots, from the tree from which God fashioned His prophets and chose His trusted ones: (a tree) of excellent wood, harmonious stature, lofty branches, flourishing limbs, ripened fruit, (and) noble interior, implanted in generosity and cultivated in a sacred precinct. There it put forth branches and fruit, became strong and unassailable, and then made him (the prophet Muhammad PBUH) tall and eminent, until God, the Mighty and Majestic, honoured him with the Faithful Spirit , the Illuminating Light , and the Manifest Book . He subjected to him Buraq and the angels greeted him. By means of him He terrified the devils, overthrew the idols and the gods (who were) worshipped apart from Him. His prophet's Wont (sunnah)is integrity, his conduct is justice and his decision is truth. He proclaimed that which was commanded by his Lord , and he delivered that with which he was charged until he made plain his mission through the profession of Unity and made manifest among the creatures that there is no god but God alone and that He has no associate; until His Oneness became pure and His lordship unmixed. God made manifest his argument through the profession of His Unity and He raised his degree with submission (al-islam). And God, the Mighty and Majestic, chose for His prophet what was with Him of repose, degree and means - upon him and upon his pure household be God's peace."