Here's a Wikipedia note on the grammar of the Kalaallisut language:
"The language, like its relatives, is highly polysynthetic and ergative. There are almost no compound words, but lots of derivations. Greenland has three main dialects: Avanersuaq (Northern Greenland), Tunu (East Greenland) and Kitaa (West Greenland).
Greenlandic distinguishes two open word classes: nouns and verbs. Each category is subdivided by intransitive and transitive words. The language distinguishes four persons (1st, 2nd, 3rd and 3rd reflexive), two numbers (singular and plural; no dual as in Inuktitut), eight moods (indicative, participial, imperative, optative, past subjunctive, future subjunctive and habitual subjunctive), ten cases (absolutive, ergative, equative, instrumental, locative, allative, ablative and prolative; for some selected nouns: nominative and accusative). Verbs carry bipersonal inflection for subject and object (distinguished by person and number). Transitive nouns carry possessive inflection."
Incidentally, here's a footnote from Robert Macfarlane's Mountains of the Mind (Granta Books, 2003, p. 177):
"On his first expedition to Greenland, Parry [William Edward Parry, 1790-1855] brought with him a flag on which was painted an olive branch. With this he hoped to convince the 'Esquimaux' of his peaceful intentions. It appears not to have occurred to Parry that the symbolic associations of an olive branch might fail to be recognized by people who lived in an ice world almost entirely devoid of vegetation, let alone of trees. It is an earlier version of the mixture of idiocy and cultural arrogance which leads some turn-of-the-millennium Englishmen abroad to believe that, if spoken very slowly, English functions as a form of intuitive Esperanto - miraculously comprehensible to all from Novosibirsk to Timbuktu."