It is refreshing to see someone who has a clear question, who seems very polite, and who is not simply relying on this website for an answer that they could easily find with a quick Google search. That being said:
Large centres of learning in the Muslim world included, but were not limited to, the cities of Baghdad, Mecca and Alexandria. In Mecca, poets and writers were known to hang their writings on walls so that citizens could read and reflect on their writings. In Alexandria, there were over 12 000 students. But Baghdad was the most impressive. In the city, there were more than 300 schools and learning institutions (a huge amount for the tenth century). These were sites of religious learning and students studied the Quran, as well as any other subjects being taught. Full time teachers were employed, and there was even a curriculum. This had a huge impact on the Islamic world, and indeed the world as we know it.
It was in these centres of learning that both the rich and poor received free education in religion. Libraries began cropping up, and foreign books were imported. The religion of Islam was the root of all this development and learning, as schools were by and large religious institutions.
Hopefully this has answered your question to an adequate degree. I am by no means an expert in Islamic history, however feel free to message me if I have left something unanswered. Please do not plagiarize this word for word, it will only decrease your learning.