Lord Caitanya then said that all the Vedic statements of the Upaniṣads aim at the ultimate truth known as Brahman. The word Brahman means "the greatest," and when we speak of the greatest we immediately refer to the Supreme Personality of Godhead, the source of all emanations.
(Teachings of Lord Caitanya).

Being so requested, Lord Caitanya explained each and every verse of Vedānta-sūtra according to the direct interpretation. He also explained the word Brahman, indicating that Brahman means the greatest, the Supreme Personality of Godhead. Brahman indicates that the greatest is full with six opulences; the Supreme Personality of Godhead is the reservoir of all wealth, all fame, all strength, all beauty, all knowledge and all renunciation.
(Teachings of Lord Caitanya).

Brahman means bṛhattva, the greatest of all. The greatest of all is Śrī Kṛṣṇa, the Supreme Personality of Godhead. He possesses all potencies and opulence in full; therefore the Absolute Truth, the greatest of all, is the Supreme Personality of Godhead. Whether one says "Brahman" or "the Supreme Personality of Godhead," the fact is the same, for they are identical.
(Sri Caitanya Caritamrta------2:6:140------purport).

The leaves and branches of the tree are also the tree, but the tree itself is neither the leaves nor the branches. The Vedic version that the whole cosmic creation is nothing but Brahman means that since everything is emanating from the Supreme Brahman, nothing is apart from Him. Similarly, the part-and-parcel hands and legs are called the body, but the body as the whole unit is neither the hands nor the legs.
(Srimad Bhagavatam------1:5:20------purport).

The Lord is described as the soul, or spirit. What is the definition of spirit? Spirit is perceivable everywhere.Brahman means "great." His greatness is perceived everywhere. And what is that greatness? Consciousness. We have personal experience of consciousness, for it is spread all over the body; in every hair follicle of our body we can feel consciousness. This is individual consciousness.
(Srimad Bhagavatam------3:26:3------purport).

Athāto brahma jijñāsā means that in order to get out of the bodily conception, one has to increase attachment to or inquiry about Brahman. Then he can be situated in the transcendental devotional service—śravaṇaṁ kīrtanaṁ viṣṇoḥ (S.B.5:7:23). To increase attachment for Brahman means to engage in devotional service. Those who are attached to the impersonal form of Brahman cannot remain attached for very long.
(Srimad Bhagavatam------4:22:21------purport).

One cannot fix one's mind upon an impersonal "something." Bhagavad-gītā (12.5) therefore says, kleśo 'dhikataras teṣām avyaktāsakta-cetasām: "For those whose minds are attached to the unmanifested, impersonal feature of the Supreme, advancement is very troublesome." Consequently, when it is said herein that King Malayadhvaja fixed his mind on Brahman, Brahman means the Supreme Personality of Godhead, Vāsudeva.
(Srimad Bhagavatam------4:28:38------purport).

One seeks happiness in impersonal Brahman, and the other seeks happiness in the association of the Supreme Personality of Godhead. As described in the first verse: brahma-saukhyam. Brahman means spiritual or eternal; both the impersonalist and the devotee seek eternal blissful life. In any case, it is advised that one become perfect.
(Srimad Bhagavatam------5:5:2------purport).

Kṛṣṇa is unlimited, His potency is unlimited, His cows and calves are unlimited, and His space is unlimited. Therefore He is described in Bhagavad-gītā as Parabrahman. The word brahman means "unlimited," and Kṛṣṇa is the Supreme Unlimited, Parabrahman.
(Srimad Bhagavatam------10:12:3------purport).