The Qur’an teaches that Islam is the continued faithful religion in the same line as the Prophets who were before Muhammad: The same religion has He established for you as that which He enjoined on Noah … and that which We enjoined on Abraham, Moses, and Jesus (42:13 AYA). The result of this view is that the scriptures given by these Prophets are considered to be genuine scriptures from God: But say, “We (Muslims) believe in the Revelation which has come down to us and in that which came down to you (Jews & Christians); our Allah and your Allah is One” (29:46 AYA).
In the Qur’an there are many references to the Jewish and Christian Holy Books. In fact the Qur’an addresses Christians and Jews in terms of the Book: O People of the Book! (5:68 AYA).
Not only Judaism in its several varieties, but hundreds of different sects of Christianity all maintain that their beliefs and practices are based on the Bible. If so many different religions can be justified by the Bible, why not Islam?
Most of Christianity recognizes the authority of the Bible, containing the Hebrew and Greek writings. There is some discussion of what writings to include and to what degree they are authoritative, but in principle Christians recognize the Bible. All forms of Judaism recognize the Torah and the other writings of the Tanach, which makes up the Old Testament of the Christian Bible.
Islam appeals primarily to the Holy Qur’an, but in principle accepts the Bible. In practice, Muslims reject the Bible on the assumption that it is corrupted from the original in order to make it accommodate to Christian teaching.The problem arises when we compare the beliefs and practices of any particular religious group with the book it appeals to. Inevitably there is much selectivity and interpretation, but beyond this remains the bare fact that the book is never the sole source of belief and practice. Where would the Christian year of festivals, the liturgy and a multitude of beliefs and practices be if all had to be founded on the Bible? Many of them would sadly fall by the wayside.