All three religions intersect with Father Abraham.
In Genesis we read that Abraham and Sarah were told by God that they will have a son:
"And God said, Sarah thy wife shall bear thee a son indeed; and thou shalt call his name Isaac: and I will establish my covenant with him for an everlasting covenant, and with his seed after him" (Gen 17:19)
Note that God said "Sarah thy wife" will bear thee a son.
As time passed there were no children conceived and since both Abraham and Sarah were too old to have kids (Abe was 99, Sarah was 90), they began to worry. The child was supposed to be Abraham's heir and through him the Shiloh, a great king who would redeem the earth would arise. But... if there was no son...
Sarah came up with what she thought was a good plan.
Gen 16:1: Now Sarai Abram's wife bare him no children: and she had an handmaid, an Egyptian, whose name was Hagar.
2 And Sarai said unto Abram, Behold now, the LORD hath restrained me from bearing: I pray thee, go in unto my maid; it may be that I may obtain children by her. And Abram hearkened to the voice of Sarai.
3 And Sarai Abram's wife took Hagar her maid the Egyptian, after Abram had dwelt ten years in the land of Canaan, and gave her to her husband Abram to be his wife.
4 And he went in unto Hagar, and she conceived: and when she saw that she had conceived, her mistress was despised in her eyes.
Hagar gave birth to a son and he was named Ishmael.
BUT remember that God had said Sarah would bear the promised child. Being Abraham's child wasn't enough. In time Sarah gave birth to Isaac.
Sarah became jealous of Hagar because the first born son always inherits the birthright, so she cast the woman out and her child...
But wait! Not so fast...
According to Islam, Ishmael was the anointed child since he was the firstborn. Furthermore, Hagar was no main! She was an important Egyptian Princess! Sarah didn't throw Hagar and her son out! Abraham left Sarah (for a time) and took them to Mecca!
In either case...
From the descendants of Ishmael came the Arabs who eventually embraced the religion of Islam (see below).
From the descendants of Isaac came the Hebrews, who later embraced the religion of Judaism (see below).
Also from the descendants of Isaac was born a Hebrew named Y'shua (or Jesus in Greek) who Christians believe was the Messiah (or Christ in Greek) of Israel (see below).
All sons of Father Abraham.
It is therefore at this pivotal moment in history that all three religions, at least in seed form, were born.
Isaac had 12 sons, the patriarchs. Moses was born from among these Hebrews during the time they were slaves in Egypt, and God gave him the Torah to lead the Jews forward. Thus was born Judaism.
The Jews believe that one day God will send a savior or messiah to save Israel and unite the world unto God. Jews are still waiting for his arrival.
Later on, a handful of Jews came to believe that Jesus was that Messiah. They promoted the idea far and wide. Since Jesus did not fulfill certain critical messianic prophecies however, the bulk of the Jews rejected his bid and he was put to death (and rose again?). After the destruction of Jerusalem in 70 CE many of these Jews fled the area and shared their faith in Jesus with non-Jews. The movement grew rapidly.
Eventually, about 300 years later, the Roman Emperor Constantine allegedly converted to the Jewish Sect of the Nazarene and declared it the official religion of Rome. He called for counsels, consisting of leaders from all the Roman religions orders. In these counsels, such as the
Nicene, the New Testament and the essential doctrines of the Universal (or Catholic) Church were set in place. Now, depending on how you figure things, the religion of Christianity either began shortly after Jesus rose the dead, circa 33 CE OR it began when the Emperor converted and
created the New Universal Religion. Most would say 33 CE.
As for the descendants of Ishmael...
They worshiped the God of Abraham for a long time, but eventually they began to embrace the gods of the people of the region, Molech, Baal, Ashteroth etc. In Mecca, at the House of God (the Ka'aba) built by Abraham and Ishmael, the Ishmaelites erect statues to all the gods and worshiped them all. Each family had their own deities, similar to the ista
devatas of India.
Then one day, Prophet Mohammed (PBUH) (570-632 CE) declared that there was but one true God, Allah subhana wa taalla and that he was God's final prophet to the earth.
While most people say that Islam was born after Christianity, Muslims argue that their religion (Ummah) was born with Abraham, which would actually make it older than Judaism (which began with Moses).
What is certain, is that all three faiths intersect with Father Abraham.
Hope this helps,