The first synagogue after exile in Babylonia 

The first synagogue ever created in the world was found in Babylonia. True, we have no exact information about it, apart from tradition, on the foundation of the "shaf Weyativ" synagogue. It relates that King Jehoiachin, who was exiled with the first deportatilon to Babylonia in 597 BCE, took earth and perhaps bricks from Eretz Yisrael, and with them build the "Shaf Weyativ" synagogue in Nehardea. (1)

According to a later tradition of the Jews in Babylonia, this is the selfsame "Great Synagogue" in Baghdad (Tslat Le-Kbiri).  R. Yosef Hayim (1897) did much to substantiate this tradition. He visited Eretz Yisrael and, on his return, brought back to Babylonia several sacks of earth and a stone. He set the stone at the entrance to the synagogue, and whoever entered through it would kiss it. He scattered the earth on the synagogue floor, which was not tiled, and thus, renewed the belief that the "Shaf Weyativ" in Nehardea is no other than the Great Synagogue in Baghdad. (2)

Adjoining the Great Synagogue, there is a large courtyard which is used as a summer synagogue for Divine worship during the hot season. This synagogue is styled by the Baghdadian Tsalat Berraniyi Li-Kbiri (outer Synagogue of the Great) (3).  The division of the synagogue into a winter and summer place of  worship was known to the Babylonian Jews of the Talmudic period. (4)

The Great Synagogue was destroyed from time to time and rebuilt. The last time that happened was in 1855, when it was rebuilt as its original design. According to R. David Sassoon, most of the synagogues in Babylonia were based on the same pattern as Tsalat El-Kbiri. 

The second synagogue in Babylonia, which is of great importance, is the "Synagogue of Hawsal"  (6).It has been taught that R.Shimon bar Yohay says: Come and see how loving Israel is before the Holy One blessed by He, for in every place of  their exile the Divine presence is with them....Where in Babylonia: Abaya says, in the "synagogoue of Hawsal" and in the synagogue of  "Shaf Weyativ" in Nehardea; now do not say here and here, but twice here and twice here. Abaya says: A blessing will come upon me when I am enter and pray there (5) 

(1) Rosh Hashana 24b.

(2) (3) M. Benayahu, 1956 - R. Sassoon David

(4) Baba Bathra, 3b.

(5) Negillah, 29b.