Photo: Hittite deity on ceramic tile at Ankara Archaeology Museum.
Most of the narratives embodying Hittite mythology are lost, and the elements that would give a balanced view of Hittite religion are lacking among the tablets recovered at the Hittite capital Hattusa and other Hittite sites: "there are no canonical scriptures, no theological disquisitions or discourses, no aids to private devotion".
The understanding of Hittite mythology depends on readings of surviving stone carvings, deciphering of the iconology represented in seal stones, interpreting ground plans of temples: additionally, there are a few images of deities, for the Hittites often worshipped their gods through Huwasi stones, which represented deities and were treated as sacred objects. Gods were often depicted standing on the backs of their respective beasts, or may have been identifiable in their animal form.
This tile surprised me strongly reminding Kali and Hindu figures. It is easier to search the traces in the roots of languages:
The Hittites were an ancient Anatolian people who spoke a language of the Anatolian branch of the Indo-European language family and established a kingdom centered at Hattusa in north-central Anatolia (on the Central Anatolian plateau) ca. the 18th century BC.
The fullest identified designation of the Hittite kingdom is "The Land of the City of Hattusa". This description could be applied to either the entire empire, or more narrowly just to the core territory, depending on context. The word "Hatti" is actually an Akkadogram, rather than Hittite; it is never declined according to Hittite grammatical rules. Despite the use of "Hatti", the Hittites should be distinguished from the Hattians, an earlier people who inhabited the same region until the beginning of the 2nd millennium BC, and spoke a non-Indo-European language called Hattic. (The conservative view is that the Hattic language is a language isolate and it is completely different from neighbouring Indo-European and Semitic languages.)
Due to its marked differences in its structure and phonology, some early philologists, most notably Warren Cowgill argued that it should be classified as a sister language to Indo-European languages (Indo-Hittite), rather than a daughter language. By the end of the Hittite Empire, the Hittite language had become a written language of administration and diplomatic correspondence. The population of most of the Hittite Empire by this time spoke Luwian dialects, another Indo-European language of the Anatolian family that had originated to the west of the Hittite region.