'Hundurinn minn' is correct, it's the nominative singular form. The genitive singular would be 'hundsins míns' (both the noun and the pronoun are declined). If 'my dog' is a subject of a sentence, most of the time the nominative is used, for example: Hundurinn minn er svartur. (my dog is black) If 'my dog' is an object... well, then comes the fun with the cases! The genitive case can be used as a possessive (similar to English): Þetta er vatnið hundsins míns. (this is my dog's water) The genitive isn't limited to that, though - several verbs and prepositions use it as well: Ég sakna hundsins míns. (I miss my dog) Ekki án hundsins míns! (Not without my dog!) I hope it's clear enough (and correct, since I'm still learning Icelandic ;))