The Songs of thanksgiving are a series of prayers that a recited during Pesukei Dezimra.
During the temple service during the days of the temple, a series of thanksgiving prayers were recited. These have since become incorporated into daily prayer.
Placement in service 
While Ashkenazi Judaism recited these following Barukh She'amar, Sephardi Judaism recites the prayers beforehand. The reason for this given by Ashkenazi Judaism is that the current world is called the World of Yezirah, a world that is not repaired, and therefore one that does not receive light from itself. Sephardi Judaism states that these prayers are recited before Barukh She'amar because the prayers receive tikkun from assiyah, as they follow Kaddish.
Prayers included 
The songs of thanksgiving are:
Hodu Lashem Kir'u Bishmo, or "Hodu" (from I Chronicles 16:8-36). This is the longer one of the thanksgiving prayers. It was first recited by David after he recovered the ark from the Philistines. Following this event, it became a standard prayer.
Psalm 100 
Psalm 100 is omitted by Ashkenazi Jews on Shabbat, Yom Tov, the Eve of Yom Kippur, the Eve of Passover, and the intermediate days of Passover. Sephardim still recite it on the Eves of Yom Kippur and Passover, and segment of them still recites it on Shabbat and Yom Tov.
On Shabbat and Yom Tov, it is omitted because offering Thanksgiving is voluntary, and therefore is not done on days with Shabbat-like restrictions.
On the Eve of Passover, it is omitted because during the temple service, one may not be able to finish eating the offering, which was chametz, before the time in which it was forbidden to eat chametz.
On Passover, it is omitted because of its chametz content.
On the Eve of Yom Kippur, it is omitted because one may not be able to finish the contents before the fast sets in.
- To pray as a Jew: a guide to the prayer book and the synagogue service By Hayim Halevy Donin, page 174-75
- Shalom Shar'abi and the kabbalists of Beit El By Pinchas Giller, page 80
- To pray as a Jew: a guide to the prayer book and the synagogue service By Hayim Halevy Donin, page 176
- To pray as a Jew: a guide to the prayer book and the synagogue service By Hayim Halevy Donin, page 175
- Jewish liturgy and its development By Abraham Zebi Idelsohn, page 82
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