There are many links between Judaism and Christianity. The first, and perhaps the most obvious, being that, according to Christian teachings, Jesus and many of his followers were originally Jewish and, therefore, the basic teachings of Christianity will be more or less equal to those of Judaism.
Judaism is, of course, much older that Christianity but there are still many similarities. Whilst Jews do not consider Christ to be the Saviour, they do believe him to be a prophet.
Each of the two faiths have their version of "Biblical Events". The Bible, of course, being the chosen material of the Christian faith and the Torah being the main method for the teaching of Judaism.
Both Christianity and Judaism are now considered to be two seperate and distinct faiths although they both have very similar origins. Both are monotheistic, believing in only a single God. This God being described similarly by Jews and Christians alike. Their teachings both including such information as "God made man in His own image". The history of both religions is almost exactly the same up until relatively recently. Both believe in the stories of characters such as Abraham discouraging people from worshipping the idols sold by his father and Moses freeing the Israelites from Egyptian rule.
There is also the belief in the "Messiah" and an afterlife, although the Jews do not believe in Jesus Christ as the Messiah as the Christians do. Christians believing that Jesus will return whilst Jews consider that there will be a new Messiah who is yet to come and will be a descendant from the House of David.
The afterlife, whilst both religions believe that there is one, there are a few differences. Christians believe that God is fair and rewards or punishes everyone with Heaven or Hell depending on how they have conducted themselves throughout this life. In Judaism, however, there is an afterlife but this is left in God's own hands.
Another major similarity is the persecution. Jews and Christians alike have been persecuted for as long as anyone knows, both suffering at different intervals at the hands of the Roman Empire as well as continued suffering which we know of within more recent history such as persecution by the Nazis in concentration camps.
Both Christianity and Judaism have survived for thousands of years and have continued to survive through adversity and both are likely to continue to do so.