Judaism, Christianity, and Islam are the three major monotheistic religions of the world. They share a common heritage and are related in many ways. However, there are also major differences between the religions.
The major similarity between these three religions is that they are all monotheistic. This means that they believe in only one God. Furthermore, many people would say that they all believe in the same God. Since they are the only three major religions in the world to believe in monotheism, this is a very important similarity.
Because the three religions believe in the same God, they also believe in some of the same scriptures. Only Judaism does not believe in the scriptures of either of the other faiths. The holy book of Judaism is the Tanakh, which corresponds closely to the Christian Old Testament. Christians believe in the authenticity of the Old Testament, but they believe that the New Testament is also the word of God. Muslims believe in the legitimacy of both the Old and the New Testaments. However, they believe that those scriptures have become corrupted in some ways and that the mistakes in those scriptures were corrected when God revealed the Quran to Muhammad. Thus, the three faiths believe in some of the same scriptures and in some different scriptures.
One major difference between the three religions is their view of the nature of Jesus Christ. To Christians, Jesus was the Son of God. He was both the Son of God and an inextricable part of God (this is a mystery of the Christian faith). Neither Jews nor Muslims believe this about Jesus. Jews believe that Jesus was a false prophet while Muslims believe that he was a true prophet but not the Son of God.
A second major difference between the two has to do with their views of Muhammad and the Quran. Muslims believe that God revealed the contents of the Quran to Muhammad. They believe that Muhammad was the last prophet of God. Neither Christians nor Jews believe that Muhammad was in any way divinely inspired.
A third difference between the three religions has to do with their vision of the nature of God. Both Jews and Muslims believe that there is only one God and that there are no distinct parts to God. Christians, however, believe that God is one God who is made up of three persons. They believe that God is simultaneously one being and three beings (God the Father, Jesus Christ, and the Holy Spirit).
There are many other differences between these religions in terms of the laws they believe in, the ways in which they practice their faiths, etc. However, these are the main theological similarities and differences between the three.