Prophet Muhammad SAW was illiterate, who wrote the Quran then?

Prophet Muhammad (Peace be Upon Him) is illiterate, how can there be al quran in first place? Who wrote it? if there is someone his friends wrote to him verses of the Quran does it still considered to be the word of Allah, or even considered to be the opinion of Prophet Muhammad SAW himself? I have this thought because my friend told me that Prophet Muhammad (Peace be Upon Him) is illiterate, sorry because I became Muslim recently.