Yes. Alot of the stories mentioned in the bible are mentioned in the Quran (Koran)

The Bible and the Qu'ran share many stories, but when you read these stories side by side many of the critical details of these stories are drastically different. These differences reflect the differing philosophical views of each religion (Islam vs. Judaism & Christianity). For example, in the Qu'ran, Abraham is asked to sacrifice his son, Ishmael, but in the Bible he is asked to sacrifice Isaac. In each story, God provides a ram to sacrifice, and promises that God will give Abraham a great nation through the son (in Islam the nation comes through Ishmael, and in Judaism and Christianity it is through Isaac). This is important b/c Muhammad traces his lineage through Ishmael, but in the Bible Abraham does not even recognize Ishmael as his son and sends him away, and the Israelites trace their lineage through Isaac. Muslims would say that these differences are because of the Hebrews and Christians corrupted the Bible, but of the thousands of ancient manuscripts that have been found, every single one of them is in total agreement theologically with the current Bible. Muhammad himself attested to the reliability of the Bible, so any corruption that would have occurred would have to have happened after Muhammad's death (otherwise he never would have said that he was sent to confirm the Bible, for why would a prophet of God confirm a book that is known to be corrupted). Since this is the case we know that the current Bible is not corrupted because we have manuscripts that predate Muhammad by several hundred years, such as the Septuagint (the greek translation of the Hebrew old Testament, which was translated at least 250 years before Jesus was born, which was 600 years before Muhammad). We also have the greek New Testament where Jesus claims to be the Son of God which also predate Muhammad's affirmation of the Bible. These texts are found throughout the Mediteranean from Rome to Babylon to Africa and would be impossible to change them all simultaneously without leaving any record of a differing text (they would not have been able to take everyone's personal Bibles that they believed in so much they were dying by the thousands to protect). In short, Muslims do not recognize all of the teachings of the Bible, but there is ample proof that the Bible is the infallible Word of God.

I would say that it is the teachings of the bible on how to lead a good life that are more important to muslims than its stories

It's a matter of the person, actually, but I'm sure they do.

Muslims recognize the Bible and it's teachings, and the Quran reiterates the the stories of the Bible. You can go to your library and read the Quran, then you will be able to decide for yourself what you think Islam is really about. When I have a question about different religions i find it useful to go straight to the source because everyone has their own opinion.

Yeah many stories run parallel in Islam, Christianity & Judaism. We hear a story from the bible and something clicks in our minds & we recognize it, but most of the stories are slightly altered. Im not sure why, i assume because there are so many different versions and analyzations of bible.