One Answer
They are monotheist religions. Which means they believe in one God. They all three also believe in the SAME God.
Most Christians know that Christianity rose from Judaism. Not as many know that Judaism does not acknowledge Jesus as the Messiah, or Son of God. Judaism believes Jesus was a false prophet and they reject His teachings. Even fewer understand that Islam believes in the teachings of Judaism and Christianity.
Muslims see their religion as simply the final word of God. Judaism being the first, then Christianity, and then Islam. Islam like Judaism does not believe that Jesus was the Son of God but they do revere Jesus as a prophet just as they do Abraham, Isaac, Noah, Moses, and the whole line of prophets including Mohammed. In Islam, just as Christianity they believe it is Jesus who will return to the earth during the final days of judgement.
It is somewhat humorous that it is Islam that accepts Christianity and Judaism. While Christians see Judaism as the fore runner to their religion and Islam as a false religion. Judaism on the other hand, does not teach that there is a single true religion, rather, that there are different paths for different people with Judaism being the path for Jews. As such, although Jews do not accept the teachings of Christianity or Islam for themselves, they see these religions as valid for other people.
Other similarities are they all sprang forth from the same region of the world and hold many of the same sites in the region as holy. This is also one of the reasons their is so much tension in the region.
Finally whether you believe me or not, all three religions are founded upon loving thy neighbor, kindness to the poor, the needy, the sick, and the outcast. They teach tolerance, patience and peace but all three have verses in their holy books that speak of murder, revenge and punishment of non-believers. I'll repeat that ALL THREE have passages in their texts that do not align with peace, love, and kindness. The main thing to remember is anyone can point to any of the three and make a case, by quoting multiple chapters and verses, that the religion is violent and intolerant. It just boils down to what an individual chooses to focus on!
Note On the Above Answer
Islam does not accept Judaism or Christianity in the sense that it condones their religious choices. Islam fervently believes that Jews and Christians are misguided and will eventually concede this and be converted to Islam. However, Islam allows for the toleration of the people in these religions because it views them as being partially correct precursors of Islam.
Islam, Judaism and Christianity.
Judaism, Christianity, and Islam have all claimed the Holy Land for themselves.
The angels in Islam are the same as the angels in CHristianity ad Judaism.
Monotheism.
Judaism, Christianity and Islam. Though Islam doesn't view Jerusalem in the same manner as Judaism or Christianity. For Judaism and Christianity, Jerusalem is place of the world's foundation and the city where G-d's presence once rested. Islam's holy city is actually Mecca, in Saudi Arabia. Islam's claim to Jerusalem is political, not religious (or at least not at all in the way Christians and Jews view Jerusalem).
Judaism, Christianity, and Islam religions.
For Judaism and Christianity it is Jerusalem. For Islam it is Mecca.
-- Islam -- Judaism -- Christianity
Christianity and Judaism
Abraham is considered the father of Judaism, Christianity and Islam as the Old Testament's 5 books of Moses - The Pentateuch (books are: Genesis, Exodus, Leviticus, Numeri and Deuteronomy) are included in the Holy Book of Judaism that is Torah. Eventually he is considered as the father of Islam basically claims entire religions of Judaism and Christianity as "prophets" and predecessors of Islam.
The question should be " What does Christianity have to do with Jews (or Judaism)?" Judaism is like a tree where Christianity is its branch and Islam is it leaves. Christianity is based on Judaism and Islam is based on Christianity. The major difference between the three is that Judaism doesn't have jesus in it unlike Christianity and Islam.
Muslims are the followers of Islam that is the religion of Allah (or God in English and same God in Christianity and Judaism). Islam is the oldest God religion in the universe. Islam means full submission to God and to His will. Islam per Torah revelation to Moses is called Judaism. Islam per the Bible revelation to Jesus is called Christianity. Islam per Quran revelation to Muhammad is called the same name Islam as it is the last God religion on earth. Accordingly, Muslims (per Quran revelation to prophet Muhammad) didn't get anything from Judaism and or Christianity. The three religions got their teachings, ritual worships, and morals from the same source that is Allah (or God in English and same God in Christianity and Judaism).