This document describes the branches and anatomy of the external carotid artery. It notes that the external carotid artery has two main branches: the external carotid artery and subclavian artery. It then provides details on several key branches of the external carotid artery and their course and blood supply, including the ascending pharyngeal artery, superior thyroid artery, lingual artery, facial artery, posterior auricular artery, occipital artery, superficial temporal artery, and maxillary artery. It also briefly describes the internal jugular vein and external jugular vein.