Gayatri Mantra
Source: Rigveda, Mandala 3, Hymn 62, Verse 10 (RV 3.62.10) — attributed to sage Vishvamitra
The "Om Bhur Bhuvah Svah" prefix commonly chanted before this verse is a vyahriti addition prescribed separately in the Taittiriya Aranyaka (2.11.1-8) — it is traditional and near-universal, but not literally part of the Rigveda verse itself.
तत्सवितुर्वरेण्यं भर्गो देवस्य धीमहि। धियो यो नः प्रचोदयात्॥
Tat savitur varenyam bhargo devasya dhimahi, Dhiyo yo nah prachodayat.
May we attain that excellent glory/effulgence of Savitr, the adorable one; may he illumine/guide our intellects.
ॐ भूर्भुवः स्वः तत्सवितुर्वरेण्यं भर्गो देवस्य धीमहि। धियो यो नः प्रचोदयात्॥
Om Bhur Bhuvah Svah, Tat savitur varenyam bhargo devasya dhimahi, Dhiyo yo nah prachodayat.
Om, [across the physical, subtle, and celestial planes] — may we attain that excellent glory of Savitr; may he illumine our intellects.
Mahamrityunjaya Mantra
Source: Rigveda 7.59.12, attributed to sage Vasishtha Maitravaruni; also recurs in the Yajurveda (Taittiriya Samhita 1.8.6.i, Vajasaneyi Madhyandina Samhita 3.60)
त्र्यम्बकं यजामहे सुगन्धिं पुष्टिवर्धनम्। उर्वारुकमिव बन्धनान्मृत्योर्मुक्षीय मामृतात्॥
Tryambakam yajamahe sugandhim pushtivardhanam, Urvarukamiva bandhanan-mrityor-mukshiya mamritat.
We worship Tryambaka, the fragrant one who nourishes and increases prosperity. As a ripe cucumber is freed from its vine, may we be liberated from death, for the sake of immortality.
Om Sahana Vavatu
Source: Taittiriya Upanishad 2.2.2 (Krishna Yajurveda); also found in the Katha Upanishad
This is an Upanishadic (Vedanta-layer) shanti mantra — canonically part of the Vedic corpus and formally attached to the Yajurveda, but a different literary layer than the Samhita-layer hymns like the Gayatri and Mahamrityunjaya mantras above.
ॐ सह नाववतु। सह नौ भुनक्तु। सह वीर्यं करवावहै। तेजस्विनावधीतमस्तु मा विद्विषावहै॥ ॐ शान्तिः शान्तिः शान्तिः॥
Om saha nav avatu, saha nau bhunaktu, saha viryam karavavahai, tejasvi nav adhitam astu ma vidvishavahai. Om shantih shantih shantih.
May we [teacher and student] be protected together, nourished together; may we work together with great energy; may our learning be brilliant and effective; may we never hate each other. Om, peace, peace, peace.
Om Purnamadah Purnamidam
Source: Opening invocation (shanti-patha) of the Isha Upanishad (Shukla Yajurveda); the same verse also appears as Brihadaranyaka Upanishad 5.1.1
Upanishadic (Vedanta-layer) shanti mantra — see note on the Sahana Vavatu entry above regarding this category distinction.
ॐ पूर्णमदः पूर्णमिदं पूर्णात्पूर्णमुदच्यते। पूर्णस्य पूर्णमादाय पूर्णमेवावशिष्यते॥ ॐ शान्तिः शान्तिः शान्तिः॥
Om purnam adah purnam idam purnat purnam udachyate, Purnasya purnam adaya purnam evavashishyate.
That is whole/infinite, this is whole/infinite; from wholeness, wholeness emerges. Taking wholeness from wholeness, wholeness alone remains.
Asato Ma Sadgamaya (Pavamana Mantra)
Source: Brihadaranyaka Upanishad 1.3.28 (Shukla Yajurveda)
Upanishadic (Vedanta-layer) shanti mantra — see note on the Sahana Vavatu entry above regarding this category distinction.
ॐ असतो मा सद्गमय। तमसो मा ज्योतिर्गमय। मृत्योर्माऽमृतं गमय॥ ॐ शान्तिः शान्तिः शान्तिः॥
Om asato ma sadgamaya, Tamaso ma jyotirgamaya, Mrityor ma'mritam gamaya.
From the unreal lead me to the real, from darkness lead me to light, from death lead me to immortality.
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