Akkadian Goddess in the Enūma Eliš
Goddess of the primordial salt sea. She was not worshipped in Mesopotamia.
Tiamat was not worshipped in Ancient Mesopotamia, nor was she considered worthy of worship. Any worship would be wholly modern.
*That is Akkadian cuneiform, her name is not recorded in any Sumerian resource I can find.
—How to use Internet Archive link
Tiāmat information on the Open Richly Annotated Cuneiform Corpus (Oracc)
From A Handbook of Gods and Goddesses of the Ancient Near East by Frayne & Stuckey [Google Book Link]:
Ti'amat, Tâmtum (page 345)
Primeval goddess, personification of the sea, in the Enuma eliš. Attested as early as the Ur III period in a theophoric name of one of the wives of Šu-Sîn. The goddess's name means "Sea" ti'amtu(m). At first, according to the Enuma eliš, Ti'amat's salt waters were co-mingled with those of her husband Apsû, the fresh waters, and together they engendered various deities, including the sky god Anu. Eventually, Ea, Anu's son, slew Apsû. Then, in a heroic battle, Ea's son, Marduk, slew Ti'amat, splitting her body in half. Marduk made one part into the vault of the heavens and the other into the surface of the earth. He made the clouds from her spittle, the mountains from her head, and the Tigris and Euphrates Rivers from her tears. She had bestowed the Tablet of Destiny on Qingu, but when Marduk defeated Qingu, he gave the tablet to Anu. There was a "seat" of Ti'amat in the temple of Marduk in Babylon, and Marduk's "seat" there was named Ti'a mat An Ugaritic lexical text equates Ti'amatu to the Mesopotamian goddess Antu(m). She occurs in an Ugaritic god list as Tihāmātu / Tamatu.
From Gods Demons & Symbols of Ancient Mesopotamian by Black & Green [Internet Archive Link]:
In the unique version of the creation of the gods preserved in the Babylonian Epic of Creation, after the separation of heaven and earth the only entities in existence were Apsû [...] and Tiamat. Apsû personified the fresh subterranean waters and Tiāmat the salt waters: the name is a form of the word tiamtum, 'sea'. Apsû and Tiāmat were envisaged as a male-female pair, although it is said that 'their waters mingled together'. They engendered a line of gods including Anu (An), Anu's son Ea (Enki) and (apparently) other deities, whose activities so disturbed Apsû that he planned to exterminate them (despite Tiāmat's protests). When Ea slew Apsû, Tiāmat determined to be avenged and created eleven monsters [...] with, as her champion, the god Qingu, described as her 'lover'. Eventually, after a heroic contest, Marduk, champion of the younger gods (in the Assyrian version his name is substituted with that of Aššur), defeated the monsters and Qingu and destroyed Tiāmat by splitting her skull with his mace, while standing on her 'lower parts'. He broke her in two 'like a dried fish', using one half to roof the heavens and the other to surface the earth: her breasts formed mountains, Tigris and Euphrates flowed from her eyes, her spittle formed clouds. While in some respects Tiāmat, like other deities, is described in anthropomorphic terms, it is difficult to form a precise picture of how the author of the Epic envisaged her. In other passages it seems to be implied that the salt sea waters were inside her.
Tiāmat's Creatures (pages 177-178)
In the Babylonian Epic of Creation, in order to avenge herself on the younger gods, Tiāmat gives birth to eleven monsters, or groups of monsters (bearing some resemblance to the Slain Heroes defeated by Ningirsu or Ninurta in a story of earlier origin). The eleven are:
the mušmahhu, ušumgallu and bašmu (three types of horned snake)
the mushuššu (a snake-dragon)
the lahamu (possibly identical to Lahmu, the long-haired ‘hero' figure)
the ugallu ('great storm-beast', the lion-demon)
the uridimmu ('raging lion', the lion humanoid)
the girtablullû ('scorpion-man': see scorpion-people)
ūmu dabrūtu ('fierce storms')
kulullû ('fish-man': see merman and mermaid)
kusarikku (a mythical beast probably derived from the bison: see bull man).
All of these are defeated by Marduk (in the Assyrian edition, Aššur) in a great battle. Images of them were placed by Marduk in the apsû (abzu) as a monument to the victory. The creatures of Tiāmat were sometimes invoked in magical incantations [...], and figurines of some of them were among those used in Neo-Assyrian protective magic, as a consequence of which their distinctive iconography can in most cases be determined.
The myth he appears in is one that justifies Marduk as chief deity and therefore legitimizes the government (at a later date it was for Aššur).
L W King Translation from 1902
Translation on Electronic Tools and Ancient Near East Archives (ETANA)
Compiled translation primarily based on E.A Speiser
E.A Speiser's translation is available in The Ancient Near East an Anthology of Texts and Pictures by James Pritchard page 28. Available on Internet Archive Library (How to use the internet archive Link)
Interesting analysis of how it represented the creation of government
Analysis from Treasures of Darkness by Thorkild Jacobsen also available on Internet Archive Library
These are academically debated as to whether or not they are Tiāmat but they are possibilities so I've included them. I have increased the contrast in both photos for visibility.
Faience, now cream probably originally glazed, cylinder seal; a standing archer (Marduk?) aims an arrow at a serpent (Tiamat?) with a crested head which rises before him. The figure wears a horizontally-striated robe and lines above his shoulder indicate arrows in a quiver. There are groups of wedges between the figures and above the serpent's coiled tail. Line border at top and bottom. — British Museum Asset Number 159745001
Black or dark brown and pale brown serpentinite cylinder seal in the linear style; a snout-nosed, horned reptile (Tiamat as a dragon?) faces left; the upper third of it's long, cross-hatched body rises vertically from two front paws or hands, one of which is raised; the remainder of the body runs around the bottom of the seal and supports three figures; there are no hind legs. A bearded god (Ninurta?) runs along the reptile's body towards the left; he wears a feather-topped head-dress and a vertically-striated, tiered and fringed open robe over a fringed kilt and has crossed, wedge-tipped quivers on his back. His arms are stretched out on either side, and in his right hand he holds a six-pronged thunderbolt below which is a rhomb, while in his left he holds two arrows. Behind the god, and advancing towards the left, is a smaller bearded god in a horned (?) head-dress with a long, tasselled streamer or necklace counterweight hanging down behind; he wears an open robe similar to that of the running god and holds a spear before him in both hands. On the tail of the reptile, with her back to the smaller god, stands an even smaller goddess, who wears a feather-topped, horned head-dress with a short tassel or necklace counterweight hanging behind, and a belted, vertically striated, tiered robe; she holds her arms open to seize the snout of the reptile. To the left of her head is a small globe-with-rays and to the right, a crescent. Line borders at top and bottom broken by the running god's head-dress. The seal may illustrate a scene from the epic of creation in which the forces of chaos, led by Tiamat, are defeated by a god representing cosmic order, probably Ninurta. Shiny, some chipping and weathering; note that there is a chip by the smaller god's shoulder and the tassel of his streamer may mask damage. — British Museum Asset Number 159863001
-not audio proof read sorry-