Close parallels can be seen in similar teachings.
Islam teaches that Jesus Christ was not crucified on the cross but His appearance came over another man who was crucified. Gnostics also believe this saying it was Simon the Cyrene who was crucified in His place.
Islam denies the Trinity in favour of One God.
Jesus is viewed as a Messenger, not the Son of God as a prophet of God.
The role of angels is an interesting one in the Quran. The demons (jinn) listened to a recitation of the Quran in Surah 72 and believed the Quran was sent down from Heaven. People have two guardian angels who record people's lives in a book which comes back on the Day of Judgement. Angels determine the fate of people on earth (see The Hadith on The Night of Power). The Court in Heaven in Judaism determines people's fate.
The soul is immortal unless God destroys it in Hell. The soul has a conscious existence after death where it is taken by the Angel of Death and his assistant. Two angels meet the soul at death taking it to the Seven Heavens. Islamic traditions also have the soul coming back to visit the funeral / and or the soul waiting by the dead body until it is buried. The soul is a spiritual copy of the physical person. The soul leaves the body at night, according to the Quran.
Since the soul has immortality, good works will determine where people live for eternity. At death the soul is taken by the two angels and meets Allah in the Seventh Heaven. Afterwards the soul is examined and a place is prepared for it, either a place of Paradise or Torment (some have this an intermediary State where the soul waits in the grave by the dead body). Others may insist the soul is kept in Heaven living another life until the Day of Resurrection.
Those who live a good life, and done righteous deeds and believe in God will enter into the Gates of Paradise. Those who are lacking in good deeds, whose balance of scales are low, will find themselves marching off to the Gates of Hell, where 19 Guardians exist (angels). These people will spend eternity in hell or as long as Allah desires. Some may be able to get a reprieve.
Early Judaism taught purgatory for the soul. Those who were considered unrighteous at the time of death would go to purgatory where they would remain until the Day of Resurrection. Most will recognise this as Catholicism. But Judaism also believes this.
Islam teaches a concept called the demiurge. "In Islamic thought, the concept of a Demiurge is actually present itself as well, particularly in Shi'ite and some Sufi orders. God being ineffable, formless, and transcendent in certain Shia and Sufi teachings, fashioned the universe through commandment to the lower beings, such as the angels. The most notable, however, are Ahlul Bayt. In some Shia teachings, the 14 Masoomeen of Ahul Bayt take the role as the Demiurge, much in the same way as I explained the Kabbalastic concept, being a council that is the manifestation of God's will in the universe and the universe's managers, even higher than all the angels. The 14 Masoomeen, particularly the 12 Imams, relay the commands and knowledge of God imparted to them by God to his creations, which would include the commands and instructions for further creation. Thus, from a certain point of view and depending on the school of Shia and/or Sufi thought, the 14 Masoomeen, or at least Muhammad (pbuh) could very well be seen as the artisans behind all creation themselves, being the first creations by whom everything else was created. Though it is important to understand that they are not gods, but merely act on the will and behalf of the One, who, through themselves, manifests itself without their sharing in his transcendent being." (source: http://www.shiachat.com/forum/topic/234998271-the-demiurge/ )
Islam speaks in favour of the Sabbath in five Surahs. The Torah is also spoken of highly in the Quran however the Rabbis are accused of tampering with the religious scriptures. This places early Islam as a Jewish Christian Gnostic sect despite its variations in the observance of the Divine Law. Allah, can be seen as a God, who changes some of the laws and does not necessarily give mankind a static unchanging torah. Charity was given to replace the enforcement of the death penalty in the Quran (with the exception of Jihad). Three compulsory Jewish prayers replaced by Five. Camel meat, although not kosher or halal was made permissible for an Arab tribe so they could eat. Allah made provision to allow the eating of non halal food in the case of starvation (same as the Jewish law to preserve life).
Islam teaches Seven Heavens, Seven Gates of Hell, and Seven Earths. Jewish Kabbalah teaches 310 worlds for the righteous, Seven Heavens and Seven Earths.
Islam is a Gnostic sect remaining in a predominately Orthodox world with the exception of magical and occult orders.
A study of Gnosticism should be done in order to help one understand the early traditions of Islam and the Quran.