The history of the Jewish community in Rome dates back to the 2nd century BCE, when the Roman Republic formed a sort of alliance with Judea under the leadership of Judas Maccabeus. At that time, many Jews came to Rome from Judea. In the following centuries, their numbers increased due to settlement related to Mediterranean trade. Later, a large number of Jews were brought to Rome as slaves after the Judean-Roman wars in Judea from 63 to 135 CE.
In 1870, after the breach of Porta Pia, the Italian army captured Rome, and the city along with its entire territory was incorporated into the Kingdom of Italy; the secular power of the popes ended. Later, Rome would be declared the capital of the Kingdom.
In the 19th century, Jews achieved full emancipation and equal civil rights, as in the rest of Europe. From that moment on, Jewish communities could erect monumental synagogues despite centuries of restrictions. It was decided to build the most impressive synagogue in the city, the Tempio Maggiore, in the same area where Jews had been confined for centuries. The Roman ghetto was destroyed, and Jews were granted citizenship. The building that previously housed the ghetto synagogue (a complex structure containing five shuls (an Italo-Jewish term for synagogues) in one building) was demolished, and the Jewish community began planning the construction of a new and impressive building.

The synagogue, designed by Vincenzo Costa and Osvaldo Armanni, was built between 1901 and 1904 on the banks of the Tiber, overlooking the former ghetto. It features elements of Assyrian-Babylonian, Egyptian, and Greco-Roman architecture. The eclectic style of the building makes it stand out even in a city known for its remarkable buildings and structures. This eye-catching design was a deliberate choice made by the community at the time, which wanted the building to become a visible symbol of their freedom and to be seen from many advantageous points in the city. The aluminum dome is the only square dome in the city, making the building easily recognizable even from a distance. The synagogue’s interior is richly decorated in the Art Nouveau style.

On October 9, 1982, a group of Palestinian commandos attacked a crowd of Roman Jews leaving the synagogue, injuring dozens of people and killing two-year-old Stefano Gaj Taché. Documents show that the secret service had informed Italian authorities of the impending danger, but no security measures were taken for the synagogue.
In 2004, the synagogue celebrated its centenary. Besides serving as a house of prayer, it is also the cultural and organizational center of the Roman Jewish community (la Comunità Ebraica di Roma). It houses the offices of the Chief Rabbi of Rome as well as the Roman Jewish Museum.
On January 17, 2005, thirteen cantors, together with the Association of Jewish Cantors of America (Chazzanim Farband), performed for the first time in the synagogue’s history at a cantorial concert.
On April 13, 1986, Pope John Paul II unexpectedly visited the Great Synagogue. This event was the first known visit of a pope to a synagogue since the early history of the Roman Catholic Church. He prayed together with Rabbi Elio Toaff, then Chief Rabbi of Rome. In 2010, Rabbi Riccardo Di Segni hosted Pope Benedict XVI. Pope Francis visited the Great Synagogue on January 17, 2016. During his visit, the pope condemned any violence committed in the name of God and joined the diaspora in a gesture of interfaith friendship. Pope Francis repeatedly echoed words first spoken by Pope John Paul, that Jews are the "elder brothers" of Christians. Pope Francis added to his words "elder sisters" of the Jewish faith.
Sources:
https://en.wikipedia.org/wiki/Great_Synagogue_of_Rome
https://museoebraico.roma.it/le-sinagoghe/