The Taittirīya Upaniṣad is one of the most practically oriented of the principal Upaniṣads — it opens with the convocation address (the teacher's parting instruction to the graduating student), moves through the Pañcakośa model (the most systematic analysis of the layers of the self in any Upaniṣad), and concludes with Bhṛgu's progressive search for Brahman. Each section is complete in itself; together they trace the full arc from ethical living through philosophical understanding to direct recognition.
The Pañcakośa — five sheaths of the Ātman
TaittU 2.2-5 contains the tradition's definitive account of the five kośas (sheaths, coverings) that envelop the Ātman:
The Brahmananda Valli — Brahman as bliss
The second section (Brahmānanda Vallī) contains two of the most important passages in the tradition. First, the Pañcakośa model (described above). Second, the account of Brahman as Ānanda (bliss) — including a remarkable mathematical exercise in TaittU 2.8 that describes bliss on a scale from human to cosmic, each level 100 times more blissful than the previous. The scale runs: human bliss → human gandharva → divine gandharva → ancestor → born-of-the-gods → gods-of-action → gods → Indra → Bṛhaspati → Prajāpati → Brahman. The purpose is not literal but philosophical: bliss is not a property Brahman possesses but what Brahman is — the scale shows that the further from the ego one moves, the greater the bliss. Source: Olivelle (1996), TaittU 2.8.
The Bhṛgu Vallī — searching for Brahman
The third section (Bhṛgu Vallī) is one of the most pedagogically elegant passages in the Upaniṣads. Bhṛgu (son of the sage Varuṇa) approaches his father: "Teach me Brahman." Varuṇa gives him only a hint: "That from which all beings are born, by which they live, and into which they return at the end — seek to know that. That is Brahman." Bhṛgu goes away and practises austerity (tapas). He returns: "Brahman is food (anna)." Varuṇa: "Practise more tapas." He returns: "Brahman is life (prāṇa)." More tapas: "mind (manas)." More: "understanding (vijñāna)." More: "bliss (ānanda)." Only with the last recognition does Varuṇa acknowledge: "So it is." The Bhṛgu Vallī is the Pañcakośa model in narrative form — the seeker moves through each sheath toward the innermost. Source: Olivelle (1996), TaittU 3.1-6.
Olivelle (1996). Gambhirananda (2004). Madhavananda (1978).
TaittU 1.11 — the convocation address in full
The Śikṣā Vallī's final section (TaittU 1.11) is the teacher's address to the graduating student — one of the earliest surviving commencement addresses in world literature and one of the most ethically concentrated. Its instructions: speak truth (satyaṃ vada); practise dharma; do not be negligent in Vedic study (svādhyāya); do not cut off the lineage of study; do not neglect truth; do not neglect welfare; do not neglect prosperity; do not neglect learning and teaching; do not neglect the rites to the gods and ancestors. Then: "Let your mother be your god. Let your father be your god. Let your teacher be your god. Let the guest be your god." The address is simultaneously a personal ethical instruction and a social-relational map: the circles of obligation ripple outward from study to family to community to the arriving stranger. Source: Olivelle (1996), TaittU 1.11.