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The Trāyastriṃśa (Sanskrit; Pāli Tāvatiṃsa; Burmese: တာဝတိံသာ [tàwədèɪɴðà]; Chinese: 忉利天, Dāolì tiān) heaven is an important world of the devas in Hindu and Buddhist cosmology. The word trāyastriṃśa is an adjective formed from the numeral trayastriṃśat, "33" and can be translated in English as "belonging to the thirty-three [devas]". It is primarily the name of the second heaven in Buddhist cosmology, and secondarily used of the devas who dwell there.
The Trāyastriṃśa heaven is the second of the heavens of the Kāmadhātu, and the highest of the heavens that maintains a physical connection with the rest of the world. Trāyastriṃśa is located on the peak of Sumeru, the central mountain of the world, at a height of 80,000 yojanas (perhaps about 400,000 miles); the total area of the heaven is 80,000 yojanas square. This heaven is therefore comparable to the Greek Olympus in some respects.
According to Vasubandhu, inhabitants of Trāyastriṃśa are each half a krośa tall (about 1500 feet) and live for 1000 years, of which each day is equivalent to 100 years of our world: that is, for a total of 36 million of our years.
Since Trāyastriṃśa is physically connected to the world through Sumeru, unlike the heavens above it, the Trāyastriṃśa gods are unable to avoid being entangled in worldly affairs. In particular, they frequently find themselves in quarrels with the Asuras, semi-divine super-human beings who were long ago expelled from Trāyastriṃśa, at the beginning of the reign of the present Śakra and who now dwell at the foot of Sumeru, plotting for ways to recover their lost kingdom. There is, however, marriage between the Trāyastriṃśa devas and the Asuras, just as there is between the Æsir and the jötnar in Norse mythology.
The chief of the Trāyastriṃśa gods is Śakra (Pāli: Sakka). Others of the Trāyastriṃśa gods who are frequently mentioned are Viśvakarman (Vissakamma), the gods' craftsman and builder; Mātali, who drives Śakra's chariot; and Sujā, Śakra's wife and daughter of the Asura chief Vemacitrin.
The Trāyastriṃśa heaven appears several times in Buddhist stories, in which either the Buddha ascends to Trāyastriṃśa, or (more often) deities from Trāyastriṃśa descend to meet the Buddha. The Buddha's mother, Māyādevī, was reborn in the Trāyastriṃśa heaven and was visited by her son, who taught her Abhidharma.
The "thirty-three" in the name of the heaven is not an enumeration of the gods who live there (there are far more) but a general term inherited from Vedic mythology, implying "the whole pantheon of gods". Hindu mythology provides a full list (with some variations) of thirty-three named deities, but it is inconsistent with the Buddhist conception and mythology of these devas.