Georgian is remarkably different from Indo-European languages. The language has several linguistic phenomena that are challenging both from theoretical and computational points of view. In addition, it is low- resourced and insufficiently studied from the computational point of view. In the thesis, we model morphology and syntax of a core fragment of the language in a formal grammar. Namely, the formal grammar is written in the HPSG framework - one of the most powerful grammar frameworks nowadays. We also implement the grammar in TRALE - a grammar implementation platform, which is faithful to "hand-written" HPSG-based grammars. Note that this is the first application of HPSG to Georgian.