1) As the Jewish communities spread and moved. This phenomenon was set in motion by the various expulsions and persecutions, which drove Jewish populations to settle in new places.
2) As non-Jews came in contact with Jews, there was a degree of influence upon them. Ancient writers speak of large numbers of people in the Mediterranean area who had taken on various Jewish practices. It was these semi-converts who were especially likely to adopt Christianity.
See also:
As Jews were exiled and moved there.
By Israel filling up with Jewish immigrants.
As the Jews began living in all the European countries.
A world map it is located in Israel.
Judaism is a religion, it all started in Abraham's time.
The way the question is written implies agency. Most of Judaism's spread was based on necessary migrations of Jews from other countries. Judaism spread by way of people moving, not populations converting. Jews spread throughout the Roman Empire, expanded out through much of Europe and also spread to the New World and Australia, before the mass return of Jews to Israel.
Judaism spread fast so equals yes
Pretty much everywhere. Judaism has even existed side by side with Islam since the time of the Prophet.
1) Through the spread of the Jewish people. Alexander was after the Destruction of the First Temple; and since the time of the First Destruction, Jews had been gradually migrating throughout the Near East, and to southern Europe, North Africa, and other regions. 2) The Greeks became aware of the Jews; and the Jewish people are given mention in Greek histories of that era.
The spread of Judaism may be called spacial distribution or diaspora. The spacial distribution of Jews differs from that of any other ethnic religion. This is because Judaism is practiced in many countries, not just its place of origin. But the spread of Judaism might be caused by diaspora, the action of when the Romans forced Jews to disperse throughout the world. The Romans had forced the diaspora after demolishing an attempt by the Jews to rebel against Roman rule.
9000BC
Judaism did not spread at all in Rome. The Ancient Romans were hostile to Jewish practice.