In the first chapter ācārya said in the first verse itself "...tatvavivekaprakāram vaksyamah" - "we shall describe the method of discriminative enquiry of truth...".
Therefore student wants to know further what is this Tattva vivekah, which the direct means for liberation.
Q: Tattvavivēkaḥ kaḥ? What is the discriminative knowledge of truth? A: Ātmā satyaṁ tadanyat sarvaṁ mithyēti I Ātmā (I) is the truth, all else other than that is mithya (apparent). The only reality is ātmā, other then that everything else is false. There are 3 words (ātmā, satyam and mithyā) we should give some explanation here. First is ātmā. Every perishable being has got an inner essence which is imperishable. Here we call it inner self - ātmā. Because of being the inner most, it is the most subtle which can not be identify with our perception. Because of unperceivable, later ācārya will explain through what is anātmā (non-ātmā) which is perceivable and being misunderstood to be ātmā all along. Next words come in-pair, satyam and mithyā. Easier to explain them through an example of gold and it's ornaments. I have a golden ring here. It is shiny, perceptible by eyes, I can feel the weight, and I can wear it on my finger also. But if we enquire further in to the truth of the ring, it is nothing but gold alone. The shine I perceived is the shine of the gold, the weight I felt is the weight of the gold, and on my finger "I am wearing gold". There is no substance called ring. Ring is a name give to a particular form of gold. When in the world of gold, a particular form or shape is made, we give them a new name. The name doesn't belong to the gold. Before being made to a ring, it was gold alone. Even now is till gold alone, but we named it ring because it is having a particular form. Therefore "ring" is a name-form principle. In Vedānta, we call it nāma-rūpa (name and form). Ring is only nāma-rūpa, but its substance is gold. Nāma-rūpa are many, but gold is only one. Just like the ring is depend on the gold for it's existence, so the name and form (and it's function) are depend on the substance to exist. In the world of gold, gold is the substance, whereas for the entire creation, ātma is the substance. That is why it is the inner self of all being, and it is the only truth of all. Other then that, everything else which is nothing but name and form is only mithyā (apparent alone) which existence depend upon satyam the truth. Therefore the existence of mithyā is borrowed existence. We can not say it is not exist, just like the ring on my finger is very real, but its existence is depend on the existence of the gold, when the gold smith melts it down, the ring does not exist anymore, what is left is just gold alone. Or we don't even need to melt it down, just bring it to resale, the shop will only see it as gold but negate the form of the ring. But the existence of the gold is not depend upon the ring or other ornaments (name and form). It is called satyam.
Gold is one, ornaments are many. Substance is one, name and form are many. Satyam is one, mithyā are many.
Ātmā is one, anātma (non-ātmā) are many.
Therefore anything in this creation other then ātmā, are name and form which having no independent existence - mithyā.
Then student wants to know more about this ātmā, where the existence of everything is depend upon which.
Q: Ātmā kah? Who is ātmā?
A: Thūlasūkṣmakāraṇa-śarīrād-vyatiriktaḥ pañcakōśātītaḥ san avasthātraya- sākṣī saccidānandasvarūpaḥ san yastiṣṭati sa ātmā.
The one who is distinct from the gross, subtle, and causal bodies, who is beyond the five levels of experience, being the witness of the three states (of experience), that which remains in the form of existence, consciousness and fullness, he is the self, ātmā.
Let us see the first one, ātmā is distinct from the gross, subtle, and causal bodies.
To answer what is ātmā, ācārya is using the approach of explaining what is anātmā (non-ātmā) first, because ātmā is un-perceivable, and anātmā is having name and form which is perceivable.
Q: Sthūlaśarīraṁ kiṁ? What is the gross body?
A: Pañcīkṛtapañcamahābhūtaiḥ kṛtaṁ satkarmajanyaṁ sukhaduḥkhādi bhogāyatanaṁ śarīraṁ. Asti jāyatē vardhatē vipariṇamatē apakṣīyatē vinaśyatīti Ṣaḍvikāravadētat sthūlaśarīraṁ.
This body made of the grossified five basic elements, born due to good karma, which is the counter for enjoyment of experiences of pleasure, pain etc., which has the six-fold modification such as exist, is born, grows, undergoes changes, degenerates and perishes, is the gross body.
Sthūlaśarīraṁ means the gross body or the physical body. The word sthūla indicate its condition which is gross. Whatever is gross means perceptible to the sense organs. There 2 kinds of cause for this physical body, one is sāmānya kāranam - general cause which is the same for every physical body, and viśesa kāranam - specific cause which is varies from individual to individual.
Now we see from the general cause first (sāmānya kāranam). The physical body is made up of five fundamental elements called pañca mahābhūtāni (pañcīkṛtapañcamahābhūtaiḥ kṛtaṁ). They are ākāśah-space, vāyuh-air, agnih-fire, āpah-water, and prthvī-earth. Not just our physical body is made of these five fundamental gross elements, also everything in the entire universe. But if everything is made with the same five fundamental element, why we all looks different even just from the point of human body? It is because of the specific cause (viśesa kāranam). This specific cause is punya (invisible result of action followed by dharma which yield pleasant situation) and pāpa (invisible result of action apposed to dharma which yield unpleasant situation) which one accumulates in countless pass life. Ācārya said satkarmajanyam kṛtaṁ - born due to good karma. How our physical looks like, animal or human, male or female, health condition etc, are determined by our karma. Even though to gain a human body, the percentage of punya and pāpa karma are about 50-50, but for gaining a human body is very difficult and precious (because only with human body, one can get moksa), therefore it said to be result of good karma.
Bhogāyatanaṁ means abode of experiences. Body is the abode for experience pleasure or pain or mixed - sukhaduḥkhādi, and it subject to modification / constant change. This modification is of six types - saḍvikāravat. They are asti-potential existence, jāyate-born, vardhate-grows up, viparinamate-plateau, apaksīyate-decay, and vinaśyati-perishes. After the body perishes, it merged back to the gross five elements.
Etat sthūlaśarīraṁ - this is gross physical body, as the explanation of anātmā (I am not).