Do Christians believe in the same God as Jews and Muslims?

This text is from a letter written by David Gooding in 1991.

Christians believe in the same God as Jews: see Hebrews 1:1-2.

Muslims believe that their God is the God and creator of all men. However, what they believe about God is very different from what both Jews and Christians believe about him.

In all their system of doctrine there is no provision for atonement. According to them, God's forgiveness is arbitrary. That is to say, God simply makes up his mind either to forgive or not to forgive, quite arbitrarily; and no one can know in advance whether God will forgive them or not. This, as you will see, is very different from the way that the Bible talks about God.

Very sincerely,