The Judaism have been living with Jews in Turkey for 2400 years. According to archeologists, there were Jewish communities even during 5th century BC.
Portugal queen Isabel had asked them either leaving the country or changing believes to Christianity in 1480. Ottoman Sultan Mehmed II had invited them to Istanbul to live together. So many Jews had migrated to Istanbul and other cities by the sea. We call them Ottoman Jews.
The Sephardic Jews have been living in the city for over 500 ears. They supported Ottoman Government much by introducing new ideas, methods and craftsmanship. The first Gutenberg press in Istanbul had been established by Sephardic Jews in 1493. They excelled many fields, particularly medicine, trade and banking. More than 20.000 Sephardic Jews still have been living in Istanbul.
Also There is Ashkenazi Jews who had come from Germany during 2nd World War. They are the followers of Judaism too. There are a few little difference in praying style.
Today, There are 20 functional synagogues in the city for Judaism. The biggest one is the Neve Shalom Synagogue was built in 1951 in the Beyoglu quarter. A decrease in the population of the Istanbul Jewish population occurred after the foundation of Israel in 1948. But the Turkish Jews who migrated to Israel helped to establish strong relationships between Turkey and Israel. The founders of Israel and prominent Israeli politicians like David Ben-Gurion, Yitzhak Ben-Zvi and Moshe Shertok had all studied in the leading Turkish schools of Istanbul namely Galatasaray High school and Istanbul University.
After the foundation Israel Country in 1948, Most of Jews had migrated to Israel. They have preferred to live in a Jewish country.