Tripura Sundari (Sanskrit: त्रिपुरा सुन्दरी, IAST: Tripura Sundarī), or Lalita is a Sanatan Dharma Hindu goddess and one of the ten Mahavidyas. She is the Shakti/consort of SadaShiva, the Prakriti to his Purusha. Lalita manifests as Goddess Sati, Goddess Parvati, Goddess Durga, Goddess Mahakali and all their incarnations, as showcased in Shakta literature. Lalita Tripura Sundari Devi is considered to be the most potent incarnation of Adi Parashakti or simply Her saguna roopa. She, along with SadaShiva is responsible for the Pancha-Krityas - Sristi or creation, Sthithi or protection, Samhara or destruction, Thirodhana or concealment of the world in Maya and Anugraha or final liberation . She is best known as the Devi glorified in the Lalita Sahasranama and as the subject of the Lalitopakhyanam (story of the goddess Lalita) in Hinduism. 
According to the Srikula tradition in Shaktism, Tripura Sundari is the foremost of the Mahavidyas and the highest aspect of Goddess Adi Parashakti. The Tripura Upanishad places her as the ultimate Shakti (energy, power) of the universe. She is described as the supreme consciousness, ruling from above Brahma, Vishnu, Rudra and Ishwara. Tripurasundari is said to sit on SadaShiva's lap in his form as Kāmeśvara, the "Lord of Desire". Tripura Sundari is also the primary goddess associated with the Shakta Tantric tradition known as Sri Vidya.
The Sanskrit word 'Tripura' is a combination of two Sanskrit words; "Tri" meaning "tráyas (three)" and "pura" meaning a city or citadel, but also understood as referring to three cities or citadels ""  referring to the legend of the three cities destroyed by Shiva. However, "Tripura" can also mean "Śiva Śaktir (Shiva Shakti)" while "sundarī" means "a beautiful woman".built of gold, silver, and iron, in the sky, air, and earth, by Maya for the Asuras, and burnt by Śiva
Therefore, "Tripura Sundarī" literally means "She who is beautiful in the three worlds".
The Tripura Sundari Temple is located in the district town of Udaipur in Tripura, about one and a half hour drive from Agartala.
She is called Tripura because she is identical with the triangle (trikona) that symbolizes the yoni and that forms her chakra (see below). She is also called Tripura because her mantra has three clusters of syllables. Here Tripura is identified with the alphabet, from which all sounds and words proceed and which is often understood to occupy a primordial place in tantric cosmology. She is three-fold, furthermore, because she expresses herself in Brahma, Visnu, and Siva in her roles as creator, maintainer, and destroyer of the universe. She is threefold also because she represents the subject (maul), instrument (mina), and object (meya) of all things. Here again, she is identified with reality expressed in terms of speech, which involves a speaker, what is said, and objects to which the words refer.
Tripura Sundari is also known by names as Ṣoḍaśī ("She who is the sixteenth"), Lalitā, Kāmeśvarī, Śrīvidyā and Raj Rajeshwari. The Shodashi Tantra refers to Shodashi as the "Beauty of the Three Cities," or Tripurasundari.
She is Tripura because she is beyond the three Gunas. She dwells in the three worlds of manas, buddhi, and chitta. She is Trayi, the unified combination of the three gods Brahma, Vishnu, and Shiva. She is also known as Lalita (the graceful one) and Kameshwari (the desire principle of the Supreme).
Details of her appearance are found in the famous hymn in her praise, the Lalita Sahasranama, where she is said to be,
seated on a throne like a queen (names 2 and 3), to wear jewels (names 13 and 14), to have the auspicious marks of a married woman (names 16–25), and to have heavy breasts and a thin waist (name 36); the crescent moon adorns her forehead, and her smile overwhelms Siva, himself the lord of desire (Kama) (name 28). She has as her seat the corpses of Brahma, Visnu, Siva, and Rudra (name 249) and is attended by Brahma, Visnu, Siva, Laksmi, and Sarasvati (name 614). She is often depicted iconographically as seated on a lotus that rests on the supine body of Siva, which in turn lies on a throne whose legs are the gods Brahma, Visnu, Siva, and Rudra. In some cases, the lotus is growing out of Siva's navel. In other more common cases, the lotus is directly on top of Shiva's lap/hips. In some less common depictions, it is growing from the Sri Chakra, the yantra.
The Vamakeshvara tantra says that Tripura-sundari dwells on the peaks of the Himalayas; is worshiped by sages and heavenly nymphs; has a body like pure crystal; wears a tiger skin, a snake as a garland around her neck, and her hair tied in a jata; holds a trident and drum; is decorated with jewels, flowers, and ashes; and has a large bull as a vehicle.
The Saundaryalahari and the Tantrasara describe her in detail from her hair to her feet. The Tantrasara dhyna mantra says that she is illuminated by the jewels of the crowns of Brahma and Visnu, which fell at her feet when they bowed down to worship her.
Shiva is one of the three gods who together constitute the Trimurti, the Hindu trinity. Shiva married Sati, the daughter of Daksha. Daksha and Shiva did not get along and consequently, Daksha did not invite Shiva for one of the great fire sacrifices that he conducted. However, Sati went to attend that function in spite of Shiva’s protest. Daksha insulted Shiva in Sati's presence, so Sati committed suicide by jumping into the fire to end her humiliation. Consequently, Shiva decapitated Daksha, but after Shiva's anger had been reduced he allowed Daksha to be resurrected with a goat’s head. This incident, i.e. death of his wife, upset Shiva and he entered into deep meditation. Sati reincarnated as Parvati, the daughter of the mountain king Himavat and his wife the apsara Mena. This was possible due to a boon was given to them by Adi Parashakti (un-manifested form of Parvati Lalita Tripura Sundari or Nirguna Brahman). Naturally, Pārvatī sought and received Shiva as her husband.
The devas faced an enemy in Tarakasura, who had a boon that he could be killed only by a son of Shiva and Parvati. So for the purpose of begetting a son from Shiva and Parvati, the devas deputed Manmatha, the god of love. Manmatha shot his flower arrows to Shiva and Parvati in order to induce love feelings in them. In anger for being tricked, Shiva opened his third eye which reduced the god of love to ashes. The devas and Rathi Devi, the wife of Manmatha, requested Shiva to give life to Manmatha. Heeding their request, Shiva stared at the ashes of Manmatha. From the ashes came Bhandasura, who made all the world impotent and ruled from the city called Shonitha pura, after which he started troubling the devas. The devas then sought the advice of Sage Narada and the Trimurti, who advised them to seek the help of Nirguna Brahman, the ultimate god head which is unmanifested i.e. Sat-Chit-Ananada (Truth-Consciousness-Bliss). Nirguna Brahman (parashivlaliha) divided itself into the male Maha Shambhu and the female Adi Parasakthi (who were unmanifested and beyond the manifest) and appeared before them. Maha Sambhu and Adi Parashakti agreed to take the forms of Maha Kameswara and Kameswari Tripura Sundari respectively, for the benefit of the universe. For this, a maha yajna (great sacrifice) was made, where the entire creation, i.e. the manifest universe, was offered as the oblation, and from the fire rose Kameshvari Tripura Sundari and Kameshvara. Tripura Sundari and Kameswara re-created the entire universe as it was before. They re-created Brahma and Saraswati, Vishnu and Lakshmi, and all the other devas. Also, as Vishnu helped Parvati attain Shiva (Tripura Sundari to marry Kameswara), Vishnu subsequently came to be known as the brother of Parvati.
Her abode also called Sri Nagara(city) had 25 streets circling it, made of iron, steel, copper, and lead. An alloy made of five metals, silver, gold, the white Pushpa raga stone, the red Padmaraga stone, onyx, diamond, Vaidoorya, Indra neela Blue Sapphire, pearl, Marakatha, coral, nine gems and a mixture of gems and precious stones. In the eighth street was a forest of Kadambas. This is presided by Syamala. In the fifteenth street lived the Ashta Dik palakas. In the sixteenth lived Varahi alias Dandini who was her commander in chief. Here Syamala also had a house. In the seventeenth street lived the different Yoginis. In the eighteenth street lived Maha Vishnu. In the nineteenth street lived Ishana, in the twentieth Tara Devi, twenty-first Varuni, the twenty-second Kurukulla who presides over the fort of pride, twenty third Martanda Bhairava, twenty-fourth Chandra, and twenty-fifth Manmatha presiding over the forest of love.
In the center of Nagara is the Maha Padma Vana (the great lotus forest) and within it, the Chintamani Griha (The house of holy thought), in the northeast is the Chid agni kunda and on both sides of its eastern gate are the houses of Mantrini and Dandini. On its four gates stand the Chaturamnaya gods for watch and ward. Within it is the chakra. In the center of the Chakra on the throne of Pancha brahmas on the Bindu Pitha (dot plank) called sarvanandamaya (universal happiness) sits Maha Tripura Sundari. In the chakra are the following decorations viz., the square called Trilokya mohanam (most beautiful in the three worlds), The sixteen petaled lotus called Sarvasa paripurakam (fulfiller of all desires), the eight petaled lotus called Sarvasamksopanam (the all cleanser), the fourteen cornered figure called Sarva saubhagyam (all luck), the external ten cornered figure called Sarvartha sadhakam (giver of all assets), the internal ten cornered figure called Sarva raksha karam (All protector), the eight cornered figure called Sarva roga haram (cure of all diseases), the triangle called Sarva siddhi pradam (giver of all powers) and the dot called Sarvananda mayam (all pleasures).
The devas prayed to her to kill Bhandasura. When she started for the war with Bandasura, she was accompanied by the powers called Anima, Mahima, Brahmani, Kaumari, Vaishnavi, Varahi, Maheshwari, Chamundi, Rudrani, Nitya Devaths and Avarna Devathas who occupy the chakra. While Sampatkari was the captain of the elephant regiment, Aswarooda was the captain of the cavalry. The army was commanded by Dhandini riding on the chariot called Giri Chakra assisted by Manthrini riding on the chariot called Geya Chakra. Jwala Malini protected the army by creating a fire ring around it. Tripura Sundari rode in the center on the chariot of Chakra. Nithya destroyed a large chunk of Bhandasura’s armies, Bala killed the son of Bhandasura, and Manthrini and Dhandini killed his brothers called Vishanga and Vishukra. When the asuras created a blockade for the marching army, Tripura sundari created Ganesha with the help of Kameshwara to remove the blockade. Then Bhandasura created the asuras called Hiranyaksha, Hiranyakashipu and Ravana. She killed all his army using Pasupathastra and killed him with Kameshwarasthra. The gods then praised her. She then recreated Manmathan for the good of the world. This story is contained in the first 84 names of the first 34 slokas of Lalitha sahasranamam. All together it contains one thousand names. This is also called the Rahasya Nama Sahasra (the thousand secret names). Reading it, meditating on the meaning of the names would lead to the fulfillment of all the wishes of the devotees.
Lalita Sahasranama contains a thousand names of the Hindu mother goddess Lalita. The names are organized in a hymns (stotras). It is the only sahasranama that does not repeat a single name. Further, in order to maintain the meter, sahasranamass use the artifice of adding words like tu, api, ca, and hi, which are conjunctions that do not necessarily add to the meaning of the name except in cases of interpretation. The Lalita sahasranama does not use any such auxiliary conjunctions and is unique in being an enumeration of holy names that meet the metrical, poetical and mystic requirements of a sahasranama by their order throughout the text.
Lalita Sahasranama begins by calling the goddess Shri Mata (the great mother), Shri Maharajni (the great queen) and Shrimat Simhasaneshwari (the queen sitting on the lion-throne). In verses 2 and 3 of the Sahasranama she is described as a Udayatbhanu Sahasrabha (the one who is as bright as the rays of thousand rising suns), Chaturbahu Samanvita (the one who has four hands) and Ragasvarupa Pashadhya (the one who is holding the rope). Chidagnikunda Sambhuta (one who was born from the altar of the fire of consciousness) and Devakarya samudyata (one who manifested Herself for fulfilling the objects of the devas) are among other names mentioned in the sahasranama.
Lalitha sahasranama is said to have been composed by eight vak devis (vaag devathas) upon the command of Lalitha. These vaag devis are Vasini, Kameshwari, Modhinee, Vimala, Aruna, Jayinee, Sarveshwari, Koulini. The sahasranama says that "One can worship Lalitha only if she wishes us to do so". The text is a dialogue between Hayagriva, an (avatar) of Mahavishnu and the sage Agastya. The temple at Thirumeyachur, near Kumbakonam is said to be where Agastya was initiated into this sahasranama. Another alternative version is the Upanishad Bramham Mutt at kanchipuram is where this initiation happened.
This sahasranama is held as a sacred text for the worship of the "Divine Mother", Lalita, and is used in the worship of Durga, Parvati, Kali, and other forms of Parvati. A principal text of Shakti worshipers, it names her various attributes, and these names are organized in the form of a hymn. This sahasranama is used in various modes for the worship of the Divine Mother. Some of the modes of worship are parayana (Recitations), archana, homa etc.
This stotra (hymn of praise) occurs in the Brahmanda Purana (history of the universe) in the chapter on a discussion between Hayagreeva and Agasthya. Hayagreeva is an incarnation of Vishnu with the head of a horse who is held to be the storehouse of knowledge. Agasthya is one of the sages of yore and one of the stars of the constellation Saptarshi (Ursa major). At the request of Agasthya, Hayagreeva is said to have taught him the thousand holiest names of Lalita. This has been conveyed to us by the sage Maharishi Vyasa. Lalitha Sahasranama is the only sahasranama composed by vag devatas under Lalitha's direction. All the other sahasranamas are said to have been composed by Maharishi Vyasa.
The slokas are organized in such a way that Devi is described from head to feet (kesadhi padham). There are basically five works (pancha krtyam). They are creation (srishti), protection (sthiti), destruction (samharam), hiding (thirudhanam) and blessing (anugraham). Devi herself has been described as "pancha krtya parayana" in the sloka and the five tasks are described as follows:
srshtikarthi brahmma roopa gopthree-govinda-rupini samharini-rudra-rupa thirodhanakareeswari sadasiva-anugrahadha panchakruthya-parayana[This quote needs a citation]
This means Devi is the aspect of Brahma, while creating sristhi, aspect of Vishnu while sustaining sristhi, aspect of Rudra during dissolution sanghara. These five entities (Brahmma, Vishnu, Rudra, Isvara and Sadasiva) are known as "pancha-brahma". Lalitha has designated the five functions to these brahmam. Sometimes, Devi will take away the life from these five brahmmam and make them inactive, performing all the five tasks herself. At that time they will be called "pancha pretam" that is lifeless bodies.The first three slokas are: Srimata (great mother) – srshti; Sri Maharajni (great ruler) – sthithi; Srimat Simhasaneswari (one who sits on the lion throne) – samharam. The rest of the slokas cover thirodhanam and anugraham.
The next names – "chidhagnikunda sambhutha devakarya samudhyatha" tells us that devi arose from the fire of knowledge to help devas in their task (war against asuras – bhandasura). From the namAa- Udhyath bhanu sahasraba till sinjanamani manjeera manditha sree padambuja, all her parts like her face, fore head, eyes, mouth, tongue, voice, hands and legs have been described.Thereafter, Devi's place (Chintamani gruham), her war against bandasura, kundalini shakti, and her properties have been described. A common image of the goddess depicts a parrot and a sugarcane with her. Sugarcane represents the sweetness of her mind.
In the Shri Vidya school of Hindu tantra, the Sri Yantra ("sacred instrument"), also Sri Chakra is a diagram formed by nine interlocking triangles that surround and radiate out from the central (bindu) point. It represents the goddess in her form of Shri Lalita Or Tripura Sundari, "the beauty of the three worlds (earth, atmosphere and sky(heaven)"(Bhoo, Bhuva and Swa).[according to whom?] The worship of the Sri Chakra is central to the Shri Vidya system of Hindu worship. Four isosceles triangles with the apices upwards, representing Shiva or the Masculine. Five isosceles triangles with the apices downward, symbolizing female embodiment Shakti. Thus the Sri Yantra also represents the union of Masculine and Feminine Divine. Because it is composed of nine triangles, it is known as the Navayoni Chakra. "These nine triangles are of various sizes and intersect with one another. In the middle is the power point (bindu), visualizing the highest, the invisible, elusive centre from which the entire figure and the cosmos expand. The triangles are enclosed by two rows of (8 and 16) petals, representing the lotus of creation and reproductive vital force. The broken lines of the outer frame denote the figure to be a sanctuary with four openings to the regions of the universe".
Together the nine triangles are interlaced in such a way as to form 43 smaller triangles in a web symbolic of the entire cosmos or a womb symbolic of creation. Together they express Advaita or non-duality. This is surrounded by a lotus of eight petals, a lotus of sixteen petals, and an earth square resembling a temple with four doors. The various deities residing in the nine layers of the Sri Yantra are described in the Devi Khadgamala Mantra.
The Shri Chakra is also known as the nava chakra because it can also be seen as having nine levels. "Nine" comes from" Nava" of Sanskrit. Each level corresponds to a mudra, a yogini, and a specific form of the Deity Tripura Sundari along with her mantra. These levels starting from the outside or bottom layer are:
The two dimensional Sri Chakra, when it is projected into three dimensions is called a Maha Meru (Mount Meru).
Her most important temple is the Kanchi Kamakshi temple in Kanchipuram, Tamil Nadu. Kanchipuram is one of the moksha puris. Sage Durvasa done intense penance in Kanchipuram and the pleased Lalita Tripura Sundari appeared and agrees to reside in Kanchi for the benefit of her devotees. Sage Durvasa installed the Sri Chakra in this temple. It is also the place of Kanchi Kamakoti mandali.
Her temple, the Tripura Sundari temple is located on top of the hills near Radhakishorepur village, a little distance away from Udaipur town in Tripura and in Banaswara, Rajasthan. In West Bengal, there is a temple of Ma Tripura Sundari Devi located in Boral, near Garia. In Madhya Pradesh, Jabalpur, there is Tripura Sundari temple about 12 km from city on Bhedaghat road in village Tewar. In the outskirts of Chennai, is the Shri Tirusoolanathar Tripurasundari temple, an ancient temple built by Kulothunga Chola I in the 11th century. The Trisula Nathar Temple is dedicated to Sri Shiva as Trisula Nathar and Divine Mother Shakti as Tripura Sundari Amman.
A temple of Tripura Sundari temple is in Chhatrabhog (Saturbhog). It is situated in south 24 Pgs under Diamond Harbour Subdivision West Bengal. The nearest railway station is Mathurapur Road in Sealdah South section. From the source of Rajratnakar descendants of Drajhu king, Kalinda made a wooden Tripura Sundari icon at this place.
Many temples of Goddess Raj Rajeshwari are also found in Uttarakhand, where she is considered as the Kul-devi. A temple of Tripura Sundari is located at tripuradevi village in Berinag.