In the Chāndogya Upaniṣad (5.1.15) it is said, na vai vāco na cakṣūṁṣi na śrotrāṇi na manāṁsīty ācakṣate prāṇa iti evācakṣate prāṇo hy evaitāni sarvāṇi bhavanti: "In the body of a living being neither the power to speak, nor the power to see, nor the power to hear, nor the power to think is the prime factor; it is life which is the center of all activities." Similarly Lord Vāsudeva, or the Personality of Godhead, Lord Śrī Kṛṣṇa, is the prime entity in everything. In this body there are powers of speaking, of seeing, of hearing, of mental activities, etc. But these are not important if not related to the Supreme Lord. And because Vāsudeva is all-pervading and everything is Vāsudeva, the devotee surrenders in full knowledge (cf. Bhagavad-gītā.
(Bhagavad-Gita-----7:19-----purport).

Those who attain the highest material planets, the planets of the demigods, are again subjected to repeated birth and death. As persons on earth are elevated to higher planets, people on higher planets such as Brahmaloka, Candraloka and Indraloka fall down to earth. The practice of sacrifice called pañcāgni-vidyā, recommended in the ChāndogyaUpaniṣad, enables one to achieve Brahmaloka, but if, on Brahmaloka, one does not cultivate Kṛṣṇa consciousness, then he must return to earth.
(Bhagavad-Gita-----8:16-----purport).

Brahmā lives for one hundred years, and his one day is calculated at 4,300,000,000 of our earthly years. His night is of the same duration. His month consists of thirty such days and nights, and his year of twelve months. After one hundred such years, when Brahmā dies, the devastation or annihilation takes place; this means that the energy manifested by the Supreme Lord is again wound up in Himself. Then again, when there is a need to manifest the cosmic world, it is done by His will. Bahu syām: "Although I am one, I shall become many." This is the Vedic aphorism (Chāndogya Upaniṣad 6.2.3). He expands Himself in this material energy, and the whole cosmic manifestation again takes place.
(Bhagavad-Gita-----9:7-----purport).

The Supreme Lord, in His localized aspect of Paramātmā, is also described in the Vedas themselves. The following verse appears in the Vedas (Chāndogya Upaniṣad8.12.3): tāvad eṣa samprasādo 'smāc charīrāt samutthāya paraṁ jyoti-rūpaṁ sampadya svena rūpeṇābhiniṣpadyate sa uttamaḥ puruṣaḥ. "The Supersoul coming out of the body enters the impersonal brahmajyoti; then in His form He remains in His spiritual identity. That Supreme is called the Supreme Personality." This means that the Supreme Personality is exhibiting and diffusing His spiritual effulgence, which is the ultimate illumination. That Supreme Personality also has a localized aspect as Paramātmā. By incarnating Himself as the son of Satyavatī and Parāśara, He explains the Vedic knowledge as Vyāsadeva.
(Bhagavad-Gita-----15:18-----purport).

The three words oṁ tat sat are uttered in conjunction with the holy name of the Supreme Lord, e.g., oṁ tad viṣṇoḥ. Whenever a Vedic hymn or the holy name of the Supreme Lord is uttered, oṁ is added. This is the indication of Vedic literature. These three words are taken from Vedic hymns. Oṁ ity etad brahmaṇo nediṣṭhaṁ nāma (Ṛg Veda) indicates the first goal. Then tat tvam asi (Chāndogya Upaniṣad 6.8.7) indicates the second goal. And sad eva saumya (Chāndogya Upaniṣad 6.2.1) indicates the third goal. Combined they become oṁ tat sat.
(Bhagavad-Gita-----17:23-----purport).

Śrī Vyāsadeva and his many disciples were all historical personalities, and they were very kind and sympathetic toward the fallen souls of this age of Kali. As such, the Purāṇas and Mahābhārata were made from related historical facts which explained the teaching of the four Vedas. There is no point in doubting the authority of the Purāṇas and Mahābhārata as parts and parcels of the Vedas. In the Chāndogya Upaniṣad (7.1.4), the Purāṇas and Mahābhārata, generally known as histories, are mentioned as the fifth Veda. According to Śrīla Jīva Gosvāmī, that is the way of ascertaining the respective values of the revealed scriptures.
(Srimad Bhagavatam-----1:4:19-----purport).

According to the Vedic version there is no existence beyond Brahman. Sarvaṁ khalv idaṁ brahma (Chāndogya Upaniṣad 3.14.1). It is stated also in the Viṣṇu Purāṇa that whatever we see is parasya brahmaṇaḥ śaktiḥ; everything is an expansion of the energy of the Supreme Absolute Truth, Brahman.
(Srimad Bhagavatam-----3:26:15-----purport).

Trying to advance in spiritual life outside the disciplic succession is simply ludicrous. It is said, therefore, ācāryavān puruṣo veda: one who follows the disciplic succession of ācāryas knows things as they are (Chāndogya Upaniṣad 6.14.2).
(Srimad Bhagavatam-----4:22:24-----purport).

In the Chāndogya Upaniṣad it is said, ācāryavān puruṣo veda: "One who approaches a bona fide spiritual master can understand everything about spiritual realization."
(Srimad Bhagavatam-----4:28:65-----purport).

We should act in such a way in this life that after giving up this body, we will become liberated from the bondage of repeated birth and death. This is called jīvan-mukti. Śrīla Vīrarāghava Ācārya states that in the Chāndogya Upaniṣad there are eight symptoms of a jīvan-mukta, a person who is already liberated even when living in this body.
(Srimad Bhagavatam-----5:4:5-----purport).

In the Chāndogya Upaniṣad it is stated: yathā saumy ekena mṛt-piṇḍena sarvaṁ mṛnmayaṁ vijñātaṁ syād vācārambhaṇaṁ vikāro nāmadheyaṁ mṛttikety eva satyam. If one studies the earth, he naturally understands the by-products of the earth. The Vedas therefore enjoin, yasmin vijñāte sarvam evaṁ vijñātaṁ bhavati (Muṇḍaka Upaniṣad 1.3): if one simply understands the original cause, Kṛṣṇa, the cause of all causes, then naturally everything else is understood, although it may be presented in different varieties.
(Srimad Bhagavatam-----5:12:8-----purport).

Brahma-saṁhitā (5.38):
premāñjana-cchurita-bhakti-vilocanena
santaḥ sadaiva hṛdayeṣu vilokayanti
yaṁ śyāmasundaram acintya-guṇa-svarūpaṁ
govindam ādi-puruṣaṁ tam ahaṁ bhajāmi
"I worship the primeval Lord, Govinda, who is always seen by the devotee whose eyes are anointed with the pulp of love. He is seen in His eternal form of Śyāmasundara, situated within the heart of the devotee." Similarly, in the Chāndogya Upaniṣad it is stated, etās tisro devatā anena jīvena. In this verse of the Chāndogya Upaniṣad the word anena is used to distinguish the ātmā and Paramātmā as two separate identities. The words tisro devatā indicate that the body of the living entity is made of three material elements—fire, earth and water. Although the Paramātmā enters the heart of the jīvātmā, who is influenced and designated by a material body, the Paramātmā has nothing to do with the jīvātmā's body.
(Srimad Bhagavatam-----5:19:4-----purport).