Types of monotheism:
Belief in Allah is the basis of faith and it is the first duty and principle of faith; and this monotheism is divided into two categories:
The first: The academic dogmatic monotheism which includes the affirmation of Allah's essence, His Names and His Attributes, and freeing Allah from Tamthil (likening Allah's Attributes to those of his creation) and likening; and this type of monotheism is divided into two categories:
(1) Tawhid-ul-Rububiyyah (Oneness of Allah's Lordship).
(2) Unity of Allah's Names and attributes.
The second: The monotheism of direction. It means: Directing the worship to Allah (may He be Exalted) alone; and this monotheism is called the oneness of divinity.
The summery is: Monotheism is divided into: Tawhid-ul-Rububiyyah (Oneness of Allah's Lordship). Unity of Allah's Names and attributes. The oneness of divinity.
Sheikh Hafizh Hakamy said:
The first obligation on people is knowing the Compassionate through monotheism because it is greater than all matters.
It is of two types to those who understand. Affirming the essence of the Lord (may He be Glorified and Exalted), His Beautiful Names and High Attributes.
Then he (may Allah bestow mercy on his soul) said:
The second type of monotheism is singling out the Lord of the Throne with worship without associating rivals to Him, to worship Allah as one god, admitting His Rights without denial. We shall handle these three types in detail without elaboration.
Tawhid-ul-Rububiyyah (Oneness of Allah's Lordship).
It implies affirming Allah's essence, and believing that He (Glory be to Him) is the true Owner, the Creator, the Provider, Sustainer, and the One who controls the Universe, and no one participates with Him in actions. First, I shall mention the proofs to Allah's essence then I shall mention the proofs on singling out Him with divinity.
A- As for the proofs on affirming His Essence, they are plenty, of which are:
First, the significance of creating the creation:
Allah (may He be Exalted) says: "Were they created by nothing, or were they themselves the creators? * Or did they create the heavens and the earth? Nay, but they have no firm Belief." [Surat At-Tur: 35 - 36].
Ibn `Abbas (may Allah be pleased with him) said: "Were they created by nothing." [Surat At-Tur: 35] i.e., without a Lord. The meaning is: Were they created without a creator? This is impossible, for their existence is a proof on their Creator. "or were they themselves the creators?" [Surat At-Tur: 35] to themselves which is not claimed by anyone, and this is impossible because they were nothing; so how could nothing create itself?
One of the bedouins was asked: What is the proof on the existence of Allah? He said: Glory be to Allah. Dung indicates a camel and a footprint indicates a march; so sky with towers, earth with paths, and seas with waves are not all these indicate the existence of the All-Aware, the Ever-Kindly. 
Second, the significance of the management of the universe:
This universe which runs in precision and creativity cannot be so precise without the existence of a Lord who manages it. Allah (may He be Exalted) says: "Verily, in the creation of the heavens and the earth, and in the alternation of night and day, and the ships which sail through the sea with that which is of use to mankind, and the water (rain) which Allâh sends down from the sky and makes the earth alive therewith after its death, and the moving (living) creatures of all kinds that He has scattered therein, and in the veering of winds and clouds which are held between the sky and the earth, are indeed Ayât (proofs, evidences, signs, etc.) for people of understanding." [Surat Al Baqarah: 164] i.e., these things are clear proofs on the Oneness of Allah, so they know that these organized items in the universe have a Creator who manages and subjugates them.
Of that also, Allah's Saying: "And among His Signs is that He created you (Adam) from dust, and then [Hawwa' (Eve) from Adam's rib, and then his offspring from the semen, and] - behold you are human beings scattered! * And among His Signs is that He created for you wives from among yourselves, that you may find repose in them, and He has put between you affection and mercy. Verily, in that are indeed signs for a people who reflect. * And among His Signs is the creation of the heavens and the earth, and the difference of your languages and colors. Verily, in that are indeed signs for men of sound knowledge. * And among His Signs is your sleep by night and by day, and your seeking of His Bounty. Verily, in that are indeed signs for a people who listen. * And among His Signs is that He shows you the lightning, for fear and for hope, and He sends down water (rain) from the sky, and therewith revives the earth after its death. Verily, in that are indeed signs for a people who understand." [Surat Ar-Rum: 20 - 24].
There are many Ayahs in this regard.
Third, the significance of people's need to Allah alone without associating partners with Him in worship:
This is confirmed in many Ayahs, of which are:
Allah (may He be Exalted) says: "Then tell Me (about) the (human) semen that you emit. * Is it you who create it (i.e. make this semen into a perfect human being), or are We the Creator? * We have decreed death to you all, and We are not unable, * To transfigure you and create you in (forms) that you know not. * And indeed, you have already known the first form of creation (i.e. the creation of Adam), why then do you not remember or take heed? * Then tell Me about the seed that you sow in the ground. * Is it you that make it grow, or are We the Grower? * Were it Our Will, We could crumble it to dry pieces, and you would be regretful (or left in wonderment). * (Saying): "We are indeed Mughramûn (i.e. ruined or have lost the money without any profit, or are punished by the loss of all that we spend for cultivation)! * (Then they said): "Nay! Indeed we are deprived of (the fruits)!" * Then tell Me about the water that you drink. * Is it you who cause it from the rain-clouds to come down, or are We the Causer of it to come down? * If We willed, We verily could make it salt (and undrinkable): why then do you not give thanks (to Allâh)? * Then tell Me about the fire which you kindle. * Is it you who made the tree thereof to grow, or are We the Grower?" [Surat Al Waqi`ah: 58 - 72].
Allah (Exalted be He) says: "Who is he besides the Most Beneficent that can be an army to you to help you? The disbelievers are in nothing but delusion. * Who is he that can provide for you if He should withhold His provision? Nay, but they continue to be in pride, and (they) flee (from the truth)." [Surat Al Mulk: 20 - 21].
Allah (Exalted be He) says: "Say (O Muhammad peace be upon him): Tell me! If (all) your water were to be sunk away, who then can supply you with flowing (spring) water?" [Surat Al Mulk: 30].
Allah (Exalted be He) says: "Say (O Muhammad peace be upon him): Tell me! If Allah made night continuous for you till the Day of Resurrection, who is an ilah (a god) besides Allah who could bring you light? Will you not then hear? * Say (O Muhammad peace be upon him): Tell me! If Allah made day continuous for you till the Day of Resurrection, who is an ilah (a god) besides Allah who could bring you night wherein you rest? Will you not then see?" [Surat Al Qasas: 71 - 72].
Fourth, the proof from the natural disposition:
Natural disposition confirms the existence of the Creator who created it, to which it resorts, and feels fear and hope to him. Allah (may He be Exalted) says: "Till when you are in the ships and they sail with them with a favorable wind, and they are glad therein, then comes a stormy wind and the waves come to them from all sides, and they think that they are encircled therein, they invoke Allah, making their Faith pure for Him Alone, saying: If You (Allah) deliver us from this, we shall truly be of the grateful." [Surat Yunus: 22].
It was previously confirmed in Ayat Al Mithaq a proof to indicate that Allah created all people knowing His Oneness.
Fifth, significance of miracles:
Of the proofs on the existence of Allah is the miracles with which He supported His Messengers.
Sheikh Ibn `Uthaymain (may Allah bestow mercy on his soul) said: The miracles of the Prophets which people watch or hear about are decisive evidences to the existence of their Sender [i.e., Allah] as they are extraordinary matters. 
Sixth, no one of the creatures has denied Allah's Lordship:
Allah (may He be Exalted) mentioned in His Book the acknowledgement of all polytheists of the divinity of their Creator. Allah (may He be Exalted) says: "And verily, if you ask them: Who created the heavens and the earth? Surely, they will say: Allâh (has created them)." [Surat Luqman: 25].
Allah (Exalted be He) says: "And if you ask them who created them, they will surely say: Allah." [Surat Az-Zukhruf: 87].
Satan himself did not deny Allah's Lordship. Allah (may He be Exalted) says in the Qur'an: "(Allâh) said: O Iblîs (Satan)! What prevents you from prostrating yourself to one whom I have created with Both My Hands." [Surat Sad: 75].
Satan did not deny that Allah created him, but he said: "[Iblîs (Satan)] said: I am better than him. You created me from fire, and You created him from clay." [Surat Sad: 76].
As for those who denied Allah's Lordship, they denied it out of haughtiness, otherwise they know that they are liars in their denial as Allah (may He be Exalted) says about them: "And they denied them (those Ayât) wrongfully and arrogantly, though their ownselves were convinced thereof [i.e. those (Ayât) are from Allâh, and Mûsâ (Moses) is the Messenger of Allâh in truth, but they disliked to obey Mûsâ (Moses), and hated to believe in his Message of Monotheism]." [Surat An-Naml: 14].
Allah (may He be Exalted) said about Moses when he was addressing the Pharaoh: "[Mûsâ (Moses)] said: Verily, you know that these signs have been sent down by none but the Lord of the heavens and the earth (as clear evidences i.e. proofs of Allâh's Oneness and His Omnipotence). And I think you are, indeed, O Fir'aun (Pharaoh) doomed to destruction (away from all good)!" [Surat Al Isra': 102].
Therefore, when the polytheists denied the call of the Messangers, the Messengers addressed them with the fact that is well-established in their natural disposition and in their minds, saying: Allah (may He be Exalted) says: "Their Messengers said: What! Can there be a doubt about Allah, the Creator of the heavens and the earth? He calls you (to Monotheism and to be obedient to Allah) that He may forgive you of your sins." [Surat Ibrahim: 10].
Seventh, the proofs of the Shari`ah:
Sheikh Ibn `Uthaymain (may Allah bestow mercy on his soul) said: As for the significance of the Shari`ah, all the codes which the Messengers brought from their Lord were full of benefits and interests for people indicate that the Sender is a Merciful and a Wise Lord; especially the Glorious Qur'an which challenged humans and jinns to bring something of the like and they failed.
 See: Tafsir Ibn Kathir, (1/ 88).
 Messages about the creed, taken from smart fruits (p. 26).
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