The Koran or Qur’an is the divinely revealed holy scripture of Islam. It was divinely revealed to Muhammad and captured in writing almost immediately afterwards.
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The Torah, or the Five Books of Moses (Genesis, Exodus, Leviticus, Numbers and Deuteronomy) is the divinely revealed holy scripture of Judaism. Unlike the Qur’an, the Torah was not committed to writing in any sort of canonical form for many centuries.
At a high level, the Torah is structured in a chronological sequence, from creation to the patriarchs to Egypt to the wilderness metamorphosis of the Israelites from slaves to a conquering people, governed by a body of laws. Of course, there are many sections of non-chronological, largely priestly ritual and law interjected throughout.
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Torah scroll
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Gutenberg Bible
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The Qur’an is not organized chronologically. It is structured into surahs ("books") by the size or length of the "books". Once you get beyond the absence of the superficial crutch of a timeline, you will read many passages that recount stories that sound very familiar--Ibrahim’s (Arabic for Abraham’s) attempted sacrifice of his son, the story of Yusuf (Arabic for Joseph) in Egypt, etc. The stories are not identical. The Qur’anic versions capture different nuances and in some parts are outright different. For example, since Muslims see themselves as descendants of Ibrahim (Abraham) through his first son, Ishmael, Ibrahim attempts to sacrifice Ishmael, instead of Isaac, as in the Jewish or Christian traditions in Genesis 22. Similarly, you will read the story of Joseph and Potifar’s wife in both texts. Interestingly, the Qur’anic version of the story captures different details.
There could be a number of explanations for these similarities. Some scholars describe the "birth of new religions" as going through an authentication period--a time when the new religion has to "prove itself" in a way. We often see this in the adoption of popular religious practices from peoples and cultures that predated the new religion. In the case of Judaism, this is apparent in the adoption of some ancient Mesopotamian practices and laws. Of course, Judaism, like all new religions, breaks new ground in numerous ways which I won’t go into here. Islam is no different. It has borrowed from practices of the Jahiliyyah period. You will find the Hajj (pilgrimage) to Makkah focusing on, among other things, the black, cubic Ka’aba, which predated Islam and was part of popular, earlier rituals. Scholars will also draw parallels to scriptural similarities. Clearly, Biblical stories were in the public domain, allowing selected portions to be adopted and incorporated into the "new religion". Since Islam follows both Judaism and Christianity, it treats both Moses and Jesus as prophets, followed by Muhammad, who is seen as the last prophet.
If you are more comfortable operating in the world of faith, rather than scholarship, you can even more easily explain the similarities between the scriptural texts. As a Jew or a Christian or a Muslim, if you open yourself to the possibility of multiple revelations, it is easy to see how one God--the same, one God--can speak to several peoples independently. God’s revelation would presumably share common messages. Different peoples might hear slightly different nuances of those messages. And, assuming that, in some cases, stories were perpetuated in oral form for centuries before they were committed to parchment, it is always possible that versions of stories evolved in part due to the frailty of human memory. The Qur’an is of special interest as it was written down very soon after it was divinely revealed.
I am a person who actually is comfortable with both of these explanations. I am comfortable with the concept of independent divine revelations which accounts for similarities and some differences in scriptural texts and beliefs. I especially like the picture of one God--the same God--guiding all of these peoples. Yet I also find the scholarly discussions of new religions borrowing practices from existing, popular rituals to authenticate themselves more than plausible. Because of man’s inherently tribal nature, we are always quick to observe the differences and distinctions. If we spent half as much time observing the similarities, the world would be a far happier place.