The maxillary artery arises from the external carotid artery and divides into three parts - the mandibular, pterygoid, and pterygopalatine parts. It supplies blood to the maxilla and mandible bones as well as structures in the face, nasal cavity, and dura mater. The maxillary artery gives off several branches along its course including the middle meningeal, inferior alveolar, deep temporal, buccal, sphenopalatine, and descending palatine arteries.