On Adhyātma-yoga in Katha 1.2.12

The wise sage, who, by means of the meditation on the inner Self, recognises the Ancient, who is difficult to be seen, who is unfathomable and concealed, who is hidden in the cave of the heart, who dwells in the abyss, is lodged in the intelligence and, seated amidst miserable surroundings indeed – renounces joy and sorrow.

~Katha 1.2.12 (tr-Chinmayananda)

taṁ durdarśaṁ gūḍhamanupraviṣṭaṁ guhāhitaṁ gahvareṣṭhaṁ purāṇaṁ, adhyātmayogādhigamena devaṁ matvā dhīro harṣaśokau jahāti.

Tam, Him - the Self that you want to know; which is durdarsam, hard to see, because of Its extreme subtleness; gudham anupravistam, lodged inaccessibly, i.e. hidden by knowledge that changes in accordance with worldly objects; guhahitam, located in the intellect- because It is perceived there; gahvares- tham, existing in the midst of misery-in the body and senses which are the sources of many miseries. Since It is thus lodged inaccessibly and located in the intellect, therefore, It is seated in the midst of misery. Hence It is hard to see. Matva, meditating on, that puranam, old (everlasting); devam, Deity- the Self; adhhatmavogadhigamena- concentration of the mind on the Self after withdrawing it from the outer objects is adhyatma-yoga--through the attainment of that; dhirah, the intelligent man; jahati, gives up; harsasokau, happiness and sorrow-since there is no excellence or deterioration for the Self.

~Shankara on Katha 1.2.12 (tr-Gambhirananda)

Adhyātma-yoga (the technique of meditation) – This is the only place where this word appears in this Upaniṣad and so it is very difficult to ascertain what Yama meant by it. As a matter of fact, this is the first occasion in the entire literature of the Upaniṣads we have the mention of ‘Yoga’ as a term. ‘Yoga’ the word, comes from the root ‘yuj’ to join or unite. Earliest usage of this root was in the sense to yoke horses, bulls and so on. It is later on that the word developed into a complete śāstra and today it has a meaning of exertion of disciplined activity of the body; and with reference to the mind, it means concentration or control through meditation. Śaṅkarācārya, therefore, combines both these meanings and says ‘yoga’ is deep meditation (samādhāna) with thoughts withdrawn from external objects.

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Meditation is the process by which a purified mind, and therefore, a highly concentrated mind, is brought to contemplate exclusively upon the nature of the Ᾱtman through a total avoidance of the mind wandering into any other object of contemplation. This process of making the mind think solely through an appointed channel of thinking, to the total effective exclusion of all dissimilar thought currents eroding in to disturb and muddy the planned channel of thought, can be successful only when the meditator is weaned away from all its gross negativities.

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Though the ordinary means and methods of getting our day-to-day objective knowledge are not available in seeking or knowing or realising Truth, there is a special method by which we can develop our powers of intuition, which are now lying dormant in us beneath the thick layers of our own fattened encrustations and by which we can experience the Ᾱtman. This technique of communion with the Self is the exact significance of the word ‘adhyātma-yoga’ here.

~Chinmayananda on adhyātma-yoga in Katha 1.2.12

Adhyaatma Yoga: There is a scientific means to realize the Self. This means is summarised by Adhigamena, which refers to the process of meditation on the Self. Since the meditation is on the Self, the Self is referred to as a Deva or ‘Deity’ being worshipped during meditation. The intellect is repeatedly brought to a focus on the inner Being. The process is well-known as just meditation, or sometimes as transcendental meditation. 

~from the Sandeepany Katha

footnote

Nisargadatta on 'Atma-yoga'

There are any number of Upanishads and yogas like hatha-yoga, Patanjali yoga, and others. But I know only atma-yoga, which is Self-knowledge and nothing else.

That is why I say my process is atma-yoga, which means Abidance in the Self. When the “non-being” state became the being state, the world, along with so many things, came into existence. As per my guru’s directive, I became one with the beingness. Beingness means having the vision that one is the entire dynamic universe. When one transcends individuality, one is the manifest beingness only. In this process the Unmanifest reveals itself.

~from Nectar of Immortality (tr-Powell)