Adhyatma is adhi plus atma. It is a spiritual discipline. Yoga is of different types, e.g., Hatha-yoga which is about various bodily postures. Here it refers to mental discipline, i.e., concentration on and awareness of the Self. It is not dependent on any external factor. Instead, it is meditation on Vedantic teachings about Self.
The Lord of death Katha mentions it (katha 1.2.12) and Shankaracharya explains. It is withdrawing the mind from the external objects and concentrating on the Self. The concentration of the mind is required because the Self is hidden (therefore hard to grasp) in the intellect surrounded by the body and senses. The body and senses are source of miseries. However, by meditating on the Self, an intelligent man perceives it in the intellect. Resultantly he goes beyond miseries, i.e., he gives up both happiness and sorrow because the Self is devoid of excellence and deterioration. It is self-evident, but it is hidden by the impressions on the mind arising from thoughts and actions. Hence the Upanishad says it is ‘hard to perceive’.

BSB 1.4.1 explains the stages. “He should merge the organ of speech into the mind” means that he should give up all the external activities of the organs of speech etc., and continue to act only through the mind; and because the mind also has a tendency to think of objects, he should discover the defect inherent in thinking of pros and cons, and then he should hold the mind confined steadfastly in the intellect that has the faculty of determination and is referred to by the term “cognizing self”. That intellect, again, he should withdraw into the great soul, the experiencer, or into the acute intellect, sharpened through meditation. The great soul is, however, to be established by him in the peaceful Self, in the supreme Purusa under consideration, that is to say, in the highest goal” (Ka. 1.3.11). [BSB Translated by Swami Gambhirananda]

Sri Krishna also instructs (BG 6.20 to 6.23). When by practice of yoga, a man controls the mind which is thus at rest, then he is fit to meditate on the Self and revels in the Self. There are utter contentment and peace. The intellect grasps infinite happiness (as distinct from experiential happiness). He identifies with and claims it. He is established in truth and is unmoved by sorrow. It is the supreme gain which can be imagined. The non-union (viyoga) from all evils is in reality union (yoga) with Self when it stands out after shedding all the superimpositions made on it due to ignorance.  This yoga is to be practiced with determination, courage and persistence. Alternatively, it implies that a yogi is not careless about concentration of mind because the mind is generally restless.

Yagnavalkya to Maitri (Br Up 2.4.5 and 4.5.6): Anything, be it husband or wife or son, etc., is loved not for its sake but for the sake of the Self. The Self should be realized by hearing, reflecting and meditating. In the Introduction to Section 1 of Chapter 4 of BSB, a doubt is raised whether the mental act is to be undertaken once only, or it is to be repeated. The aphorist says (BS 4.1.1), “Repetition is necessary, since the Upanishads instruct repeatedly.” Sri Shankara comments, “—-these have to culminate in the intuitive realization of Brahman; for hearing etc. fulfil their purpose of producing a (tangible) perceptible result in this case when they culminate in realization through repetition, even as husking etc. culminate in producing rice etc. Besides, by the word upasana (continuous remembrance, adoration) and nididhyasana (profound meditation) are implied acts involving this aspect of repetition.” [BSB Translated by Swami Gambhirananda]

The opponent counters (BSB 4.1.2) that if the hearing of “That thou art” (Ch. 6.8.7) once does not result in the realization of the unity of Self, then even repetition is not expected to produce it.  The commentator clarifies that repetition will be unnecessary for one who can realize the Self as Brahman after hearing “That thou art” once only. But for one who cannot do so, a repetition is a necessity. Uddalaka teaches (Ch 6.8.7) Svetaketu, ‘Tat tvam asi’ and the latter requests, “0 revered sir, explain to me again”. Uddalaka removes the respective causes of Svetaketu’s misconceptions and teaches repeatedly. “That very process is referred to in the text, “It is to be heard of, reflected on, and meditated upon (Br 4.5.6).” [BSB Translated by Swami Gambhirananda]