The absolute oneness of Allah is primary to Muslims. The greatest sin is to associate any partner with him. The sin is called shirk. Muhammad’s message, advocating one God, was courageous, because idolatry was the established religion of Arabia. Muhammad challenged this system, and finally prevailed with the message of monotheism. Islam is rooted in this commitment to the belief in one God.
The Bible teaches that God is one, but His is a complex unity, not just a simple unit. He is completely unique---a personal God Who existed in relationship from eternity.
In Islam, Allah is transcendent and cannot be compared to humans or any other created thing. Allah’s character and attributes are revealed through his 99 Arabic names, the two most common being “The Merciful” and “The Compassionate.” Allah is never described in Islam by using human family terms such as “father” or “son.” In the Qur’an, he reveals his will for mankind to obey, not his person for mankind to relate with and know.
In the Bible, which is the Christian’s authority, the Scriptures reveal God as the ultimate Father, in name, character, and person, but always as the Creator, never with sexual references. God is called “Father” in a spiritual sense, not in a literal, biological sense. God also reveals Himself as the Eternal Word, Who became flesh when the Holy Spirit overshadowed the Virgin Mary and conceived Jesus, the Messiah, Who is also called the Son of God in the Bible. In His teaching, Jesus further reveals God the Holy Spirit, Who was sent by the Father and Himself. The Bible presents a mystery of three Persons revealed as one God. Although the world “Trinity” is not in the Bible (just as the word tawhid, which means the unity of God, is not in the Qur’an), the term captures biblical truths about God. The Father, Son and Holy Spirit are God, not just three parts of God or three names for the same person. Not a council of gods, but a supreme, unique Being Who is different from (and above) every creature, Who exists as a tri-unity of Persons. God exists as one Being Who is three Persons. People do not exist in this way; only God exists in this way.
In Islam, Allah creates and sustains all life, spiritual and material. His will is absolute and cannot be questioned by his creation. He is the final judge, without a mediator. The best chance on Judgment Day is for those who live lives of righteousness and submission to Allah’s will---Insha Allah (God willing).
The Bible says, “God is Love.” This love existed from eternity as the Father loved the Son, even before the foundation of the world. God’s love is expressed through creation. God does not simply choose to love; His love chooses to act. “God so loved the world that He gave His Son…” (John 3:16)
Most Muslims consider Christians to be polytheists (people who believe in many gods) because of the Trinity. A popular misunderstanding of the Trinity is that Christians believe that a Father God had sex with a Mother God (Mary) to produce their “Son of God.” No Christian believes this. Educated Muslims understand this false Trinity is not what Christians believe, but they still do not understand how the math can show God’s unity. To them, it is simple: 1+1+1=3; Father + Son + Holy Spirit = Three Gods. But this is not what Christians believe, either.
Rather than using an analogy of adding units (1+1+1=3), the Trinity has been explained as multiplied wholeness (1x1x1=1). The Bible says Jesus is the eternal “Word of God” revealed in flesh through the virgin birth. The Qur’an sets apart Jesus as the “Word of God” and “Spirit of God” and affirms His virgin birth and miracles, even raising the dead. Muslims also believe in the Second Coming of Jesus, because the “day of his return” is mentioned in the Qur’an. Muslims like to point out how the Qur’an honors Jesus. Yet, such positive references to Jesus in the Qur’an are few, compared to the complete story of Jesus preserved by God in the Injil (New Testament).
(Most of this information is from "Islam & Christianity," Rose Publishing)