For knowing the theory of knowledge according to the Quran, you have to study this verse: “Bring me a Book revealed before this or some other vestige of knowledge, if you are telling the truth.” (46:4).
According to this verse, the Quranic theory of knowledge is based on two points. First, revealed knowledge, and second the knowledge established by any branch of science. According to the Quran, both the sources are valid. But, there is a difference. Scientist studies the physical universe. The concern of science is nothing other than the physical world. Due to this, it is accepted among scientists that science gives us but a partial knowledge of reality.
If anything is established by scientific studies or by experimental studies it will be acceptable to Islam, provided it is not only a theory but an established fact. For example, the concept of organic evolution is not acceptable in Islam. Because, it is not based on scientific facts in the real sense, but is adopted only as a workable theory.
Then there is a question. According to Bertrand Russell, there are two kinds of knowledge: knowledge of things and knowledge of truth. Knowledge of things can be achieved through science, but knowledge of truth does not fall in the domain of science. Although we need to have knowledge about this field, but science does not provide help in this regard.
The other branch of knowledge is philosophy. Philosophy is still midway, it is not in the position to provide satisfactory answers to the basic questions regarding existence. It is this fact that is mentioned in the Quran in these words: “You have been granted but little knowledge.” (17:85)
In such a situation, the Quran invites people to go through the revealed knowledge preserved in the Quran. Revealed knowledge gives us knowledge regarding that branch where science and philosophy do not help us.
Islam doesn't claim that revealed knowledge can be justified in the same way as science, which is verifiable knowledge. But, there is another method, that is, inferential method. And, if you apply the inferential method of study, you can reach the truth.
If you are interested in studying this point of view in detail, please refer to my these two books: God Arises and Religion and Science.