The Quran was revealed by Allah, not created
Question

Can you recommend a book in english that explains what it really means that the Quran is not a creation ; and what we should believe in as Muslims?
Praise be to Allah.What we Muslims are obliged to believe is that which has come to us from Allah, and that which the Messenger of Allah (peace and blessings of Allah be upon him) has told us. Allah has told us that He speaks, as He says (interpretation of the meaning): 
“And who is truer in statement than Allah?[al-Nisaa’ 4:87] 
“and whose words can be truer than those of Allah?
[al-Nisaa’ 4:122] 
These two aayahs offer proof that Allah speaks, and that His words are true, and there is no kind of lie in them at all. 
Allah says (interpretation of the meaning): 
“And (remember) when Allah will say (on the Day of Resurrection): ‘O ‘Eesa (Jesus), son of Maryam (Mary)!…’”
[al-Maa’idah 5:116] 
This aayah shows that Allah speaks, and that His speech can be heard, so His speech has sound. And His speech includes words and phrases. The evidence that the speech of Allah is composed of letters is the aayah (interpretation of the meaning):  
“O Moosa (Moses)!
Verily, I am your Lord!”[Ta-Ha 20:11] 
because these words are composed of letters, and they are part of the speech of Allah. And the evidence that the speech of Allah has sound is the aayah (interpretation of the meaning]: 
“And We called him from the right side of the Mount, and made him draw near to Us for a talk with him [Moosa (Moses)].
[Maryam 19:52] 
Calling and talking can only happen with sound. 
See Sharh Lam’ah al-I’tiqaad by Ibn ‘Uthaymeen, p. 73 
Hence the belief of Ahl al-Sunnah wa’l-Jamaa’ah is that Allah speaks in a real sense, when and as and with whatever He wills, with letters and sound, but this does not resemble the voices of created beings. The evidence that it does not resemble the voices of created beings is the aayah (interpretation of the meaning): 
“There is nothing like Him, and He is the All‑Hearer, the All‑Seer”[al-Shoora 42:11] 
So it is known from the outset that this is the belief of Ahl al-Sunnah wa’l-Jamaa’ah. Ahl al-Sunnah wa’l-Jamaa’ah believe that the Quran is the word of Allah, and among the evidence for this belief is the aayah (interpretation of the meaning): 
“And if anyone of the Mushrikoon (polytheists, idolaters, pagans, disbelievers in the Oneness of Allah) seeks your protection then grant him protection so that he may hear the Word of Allah”
[al-Tawbah 9:6] 
what is meant here is the Quran, by scholarly consensus. The fact that Allah mentions kalaam (speech, word) in idaafah (genitive or possessive construction) with Himself  indicates that the Quran is His Word. 
The belief of Ahl al-Sunnah wa’l-Jamaa’ah is that the Quran is the word of Allah which was revealed, not created; it began from Him and will return to Him.  
The evidence that it is revealed is as follows (interpretation of the meanings): 
“The month of Ramadan in which was revealed the Quran”
[al-Baqarah 2:185] 
“Verily, We have sent it (this Quran) down in the Night of Al‑Qadr (Decree)”[al-Qadr 97:1] 
“And (it is) a Quran which We have divided (into parts), in order that you might recite it to men at intervals. And We have revealed it by stages”[al-Israa’ 17:106] 
“And when We change a Verse (of the Quran) in place of another — and Allah knows best what He sends down — they (the disbelievers) say: ‘You (O Muhammad) are but a Muftari! (forger, liar).’ Nay, but most of them know not.
Say (O Muhammad) Ruh‑ul‑Qudus [Jibreel (Gabriel)] has brought it (the Quran) down from your Lord with truth, that it may make firm and strengthen (the Faith of) those who believe, and as a guidance and glad tidings to those who have submitted (to Allah as Muslims).
And indeed We know that they (polytheists and pagans) say: ‘It is only a human being who teaches him (Muhammad).’ The tongue of the man they refer to is foreign, while this (the Quran) is a clear Arabic tongue[al-Nahl 16:101-103] 
- the One Who changes a verse in place of another is Allah, may He be glorified and exalted. 
The evidence that the Quran is not created is the aayah (interpretation of the meaning): 
“Surely, His is the creation and commandment”[al-A’raaf 7:54] 
So Allah describes creation as one thing and commandment as another. The conjunction implies that the second thing mentioned is different, and the Quran is part of the commandment because of the evidence of the aayah (interpretation of the meaning): 
“And thus We have sent to you (O Muhammad) Rooh (a revelation, and a mercy) of Our Command. You knew not what is the Book, nor what is Faith? But We have made it (this Quran) a light wherewith We guide whosoever of Our slaves We will”
[al-Shoora 42:52] 
If the Quran is part of the command or commandment, which is different from creation, therefore it is not created, because if it were created, this division of categories would not be correct. This is the evidence from the Quran. 
The rational evidence is that the Quran is the word of Allah, and words cannot exist in and of themselves so that they would have a distinct and separate identity.  If they did exist separately and distinct from Allah, then we would say that they are created, but words are an attribute of the speaker. If they are an attribute of the speaker and they are spoken by Allah, then they are not created, because the attributes of Allah are not created. 
Sharhal-‘Aqeedah al-Waasitah by Ibn ‘Uthaymeen, 1/418-426-441  
We must believe this and be certain of it. We should not change the meanings of the verses of Allah, for they clearly indicate that the Quran is a revelation from Allah. Hence Imaam al-Tahhaawi (may Allah have mercy on him) said: “The Quran is the word of Allah which came from Him in the form of speech, without any need for us to know how. He sent it down to His Messenger by Revelation, the believers believe that it is true and they are certain that it is indeed the word of Allah and that it is not created like the words of human beings. Whoever hears it and claims that it is the words of human beings is a kaafir, who is condemned and warned of Hell, as Allah says (interpretation of the meaning):
‘I will cast him into Hell fire’ [al-Muddaththir 74:26]. 
Since Allah threatened with Hell the one who said, ‘This is nothing but the word of a human being’ [al-Muddaththir 74:26 – interpretation of the meaning], we know and are certain that it is the word of the Creator of mankind, and it does not resemble the speech of human beings.”  Sharh al-‘Aqeedah al-Tahhaawiyyah, 179