There is not simply a “link” between Judaism and Christianity. Jesus said that He did not come to abolish the Law (Torah, the central object of study in Judaism), but to fulfill the Law. In other words, everything he taught and did flowed from the TaNaK’s teachings. He claimed that He was the God the TaNanK spoke of (John 8:58). He claimed that the TaNaK prophesied about himself, and all that he did (Luke 24:27). Christianity in it’s purest form (1st century AD) should be understood as a small sect of Judaism. Before the New Testament scriptures were ever written, all the early Christians had was the TaNaK. All of their preaching and evangelism came from Jesus’ teachings (which in the later half of the 1st century began to be written down) and the TaNaK.
To say they are merely “linked” is incorrect indeed. Christianity should be seen as a continuation and fulfillment of ancient Judaism (pre-rabbinic). Jesus was the bridge that would connect the two.
A study of the New Testament scriptures in purity, apart from modern liberal scholarly opinion (which tries with all of it’s effort to preach the New Testament as inauthentic and invalid), and even apart from modern conservative opinion, you will see that all of it’s teachings are rooted inside of the TaNaK. Some claim that the Apostle Paul, the man who wrote the majority of the New Testament, “invented” Christianity’s doctrines and beliefs. How far this is from the truth! The TaNaK is quoted hundreds of times in the New Testament. All of Paul’s teachings finds root in the TaNaK scriptures (which is, by the way, the Christian’s Old Testament scriptures).
To understand Christianity is to understand what ancient Judaism taught. Jesus came and helped us understand what ancient Judaism taught. He came and helped us understand what the prophets of old meant by the things they said. He came and helped us understand the actual purpose of the Law, and the intentions God had through the Law. What he taught completely invalidated rabbinic Judaism, and this led to his death.
It is said indeed that Christianity has been pushed farther and farther away from it’s roots. Every time I see a copy of the New Testament by itself, away from the Old Testament, I cannot help but ask the question “But how can one understand the New Testament without the Old Testament?” In other words, how can one understand the teachings of Christianity apart from the teachings of ancient Judaism? I would argue that we cannot. They are inextricably linked. It is hard to see this today, as the Judaism we know of today is nothing but a reform version of ancient rabbinic Judaism, which is very much a product of the exile in 586 B.C. Judaism, in the first exile, was forced to reform itself, as the Temple no longer stood, and as they were no longer dwelling in Jerusalem. The Temple is unable to be separated from ancient Judaism. The Temple is unable to be separated from Jerusalem. Therefore, with the two missing from their lives, they were forced to reform Judaism, and all of it’s teachings. What we were left with was 1st century Rabbinic Judaism. This reformed Judaism then experienced another reform after the destruction of the Temple in 70 A.D. Now, what we are left with today is a reformed version of a reformed version of Judaism that in it itself has experienced numerous reforms! Traces of Christianity are almost distinct from modern Judaism, as modern Judaism is becoming more and more separated from their bible, the TaNaK.
In short, it can be summarized as this – Ancient Judaism and Christianity have one link. This link is Jesus. Today’s Judaism is not what ancient Judaism was. Although it is difficult to find traces of Christianity inside of modern Judaism, we can be sure that Christianity is what ancient Judaism was originally intended to evolve into, through the person and work of Jesus Christ.
The real “link” per-say between Judaism and Christianity is Jesus.