This research project studies Enindhilyakwa (also known as Anindilyakwa), spoken by about 1500 people on Groote Eylandt, Northern Territory, Australia. It has two main aims: (1) documentation and analysis of the complex morpho-syntax of this language; and (2) development of a learner’s grammar that can be used for language maintenance and future literacy programs. Enindhilyakwa is a polysynthetic language, allowing a high degree of complexity in its word structure. It is endangered because of cultural breakdown, illiteracy, lack of teaching material and growing influence of English. This is manifested in the fact that the more complex forms are no longer being used by younger speakers today. This project focuses on the documentation of this morpho-syntactic complexity. Capell (1942:376) considered Enindhilyakwa, together with the neighbouring language Wubuy (aka Nunggubuyu), to be “the [two] most complicated languages in north Australia, perhaps in the whole of Australia”, which may be due to the interaction of the phonological system and the rich morphology. Much of the morphological richness of this language is currently under threat of being lost, as many of the more complex forms are no longer used by the younger generations. By comparison with most Australian languages, Enindhilyakwa has many speakers, so it has a good chance of survival. The chances will be increased by heightening the community’s awareness through their involvement in a good documentation programme, and through providing resources which they can use in language maintenance, such as a learner’s grammar.