Akshividya is a branch of learning in spiritual knowledge. Akshi Vidya is described in the fourth chapter of Chandogya Upanishad and a detailed discussion about it is available in the Antaradhikarana of Brahmasutra Bhashya.
Akshividya relates to the purusha (being) residing in akshi (eye).
Chandogya Upanishad refers to purusha who is seen with the eyes as the soul; who is deathless and fearless, and who is verily the Brahman. He is untainted by any blemish just like his locus, the eye, which is not tainted by the drops of water or ghee falling in it, as they roll off the eye. Here, the meditation is not on the external eye but on the being within, which is none other than our own soul. He is called samyadvama, as all fruits of actions on account of him. He is called vamani too, as he bestows auspicious things on the jiva. He is also described as bhamani, since he illuminates all objects.
The fruit of Akshividya is that all adorable objects merge in the upasaka (practitioner) (which means, the acquires them), and he becomes effulgent. He travels through the devayana path and is guided by amanavapurusha (a superhuman being) to the saguna Brahman and does not return to the human world again.