Which artery is not a branch of the internal carotid artery?

The maxillary artery is indeed not a branch of the internal carotid artery. It is a major branch of the external carotid artery, which supplies deep structures of the face, the maxilla, and the mandible, among other areas.

In contrast, the anterior cerebral artery, middle cerebral artery, and anterior choroidal artery are all branches that originate from the internal carotid artery. The anterior cerebral artery supplies blood to the medial portion of the frontal lobes and the superior medial parietal lobes. The middle cerebral artery, which is the largest branch of the internal carotid artery, supplies a significant portion of the lateral cerebral surface, including areas critical for speech and motor function. The anterior choroidal artery provides blood to the choroid plexus, parts of the thalamus, and other essential areas.

This understanding of the branches of the internal and external carotid arteries is fundamental in clinical practice, as conditions affecting blood supply can have significant implications for brain function and pathology.