The concept of avatar within Hinduism is most often associated with Vishnu, the preserver or sustainer aspect of God within the Hindu Trinity or Trimurti of Brahma, Vishnu and Shiva. Vishnu's avatars descend to empower the good and fight evil, thereby restoring Dharma. Traditional Hindus see themselves not as "Hindu", but as Vaishnava (Worshippers of Vishnu), Shaiva (Worshippers of Shiva), or Shakta (Worshipper of the Shakti). Each of the deities has its own iconography and mythology, but common to all is the fact that the divine reality has an explicit form, a form that the worshipper can behold. An oft-quoted passage from the Bhagavad Gita describes the typical role of an avatar of Vishnu:

Arjuna, whenever righteousness is on the decline, unrighteousness is in the ascendant, then I body Myself forth. For the protection of the virtuous, for the extirpation of evil-doers, & for establishing Dharma (righteousness) on a firm footing, I manifest Myself from age to age. — Bhagavad Gita 4.7–8

The Vishnu avatars appear in Hindu mythology whenever the cosmos is in crisis, typically because evil has grown stronger and has thrown the cosmos out of its balance. The avatar then appears in a material form, to destroy evil and its sources, and restore the cosmic balance between the ever-present forces of good and evil.

The most known and celebrated avatars of Vishnu, within the Vaishnavism traditions of Hinduism, are Krishna, Rama, Narayana and Vasudeva. These names have extensive literature associated with them, each has its own characteristics, legends and associated arts. The Mahabharata, for example, includes Krishna, while the Ramayana includes Rama.
The Bhagavata Purana describes Vishnu's avatars as innumerable, though ten of his incarnations, the Dashavatara, are celebrated therein as his major appearances. The ten major Vishnu avatars are mentioned in the Agni Purana, the Garuda Purana and the Bhagavata Purana.

The ten best known avatars of Vishnu are collectively known as the Dashavatara (a Sanskrit compound meaning "ten avatars"). Five different lists are included in the Bhagavata Purana, where the difference is in the sequence of the names. Freda Matchett states that this re-sequencing by the composers may be intentional, so as to avoid implying priority or placing something definitive and limited to the abstract.
The Bhagavata Purana also goes on to give an alternate list, wherein it numerically lists out 23 Vishnu avatars in chapter 1.3.
199 Four Kumaras (Catuḥsana): the four sons of Brahma who exemplify the path of devotion.
299 Varaha: The boar avatar. He rescues Bhumi, the goddess of the earth, when the asura Hiranyaksha abducts her, restoring her rightful place in the universe.
399 Narada: the divine-sage who travels the worlds as a devotee of Vishnu.
499 Nara-Narayana: the twin-sages.
599 Kapila: a renowned sage spoken of in the Mahabharata, son of Kardama and Devahuti. He is sometimes identified with the founder of the Samkhya school of philosophy.

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Although Puranic scriptures contain occasional references to avatars of Shiva, the avatar doctrine is neither universally accepted nor commonly adopted in Shaivism. The views on the doctrine of incarnation has been one of the significant doctrinal differences between Vaishnavism and Shaivism, in addition to their differences on the role of householder life versus monastic life for spiritual release. Shaivism is a transcendental theology, where man, with the help of his Guru, is his own savior.

The Linga Purana lists twenty-eight avatars of Shiva. In the Shiva Purana there is a distinctly Saivite version of a traditional avatar myth: Shiva brings forth Virabhadra, one of his terrifying forms, in order to calm Narasimha, an avatar of Vishnu. When that fails, Shiva manifests as the human-lion-bird Sharabha which calms down lion-man Narasimha avatar of Vishnu, and Shiva then gives Vishnu a chakra (not to be confused with Sudarshan Chakra) as gift. A similar story is told in the late medieval era Sharabha Upanishad. However, Vaishnava Dvaita school refutes this Shaivite view of Narasimha. According to the Shiva Purana, Shiva has 19 avatars. According to the Kurma Purana, he has 28.

The vanara god Hanuman who helped Rama (the Vishnu avatar) is considered by some to be the eleventh avatar of Rudra (Shiva). Some regional deities like Khandoba are also believed by some to be avatars of Shiva. Ashwatthama, the son of Drona is also considered to be an avatar of Shiva.

Shesha and his avatars (Balarama and Lakshmana) are occasionally linked to Shiva. Adi Shankara, the formulator of Advaita Vedanta, is also occasionally regarded as an avatar of Shiva.

In Dasam Granth, Guru Gobind Singh mentioned two avatars of Rudra: Dattatreya Avatar and Parasnath Avatar.

Avatars are also observed in Shaktism, the sect dedicated to the worship of the Goddess (Devi), but they do not have universal acceptance in the sect. The Devi Bhagavata Purana describes the descent of Devi avatars to punish the wicked and defend the righteous as – much as the Bhagavata Purana does with the avatars of Vishnu.

Nilakantha, an 18th-century commentator on the Devi Bhagavata Purana – which includes the Devi Gita – says that various avatars of the Goddess includes Shakambhari and even the masculine Krishna and Rama – generally thought to be Vishnu's avatars. Parvati, Lakshmi and Saraswati are main goddesses worshipped as Devi avatars.
Devi is popular in her form as Parvati. In Devi Mahatmya she is seen as the Goddess Mahakali, and in Uma Samhita, she is seen as Devi herself. Regarding her incarnations, it varies per sect in Hinduism. She could be all Goddesses as said in Shaivism and some main Shatism interpretations like the Sri kula and Kali Kula families, or just a form of Devi in some other Shaktism interpretations and many Vaishnava interpretations. With this in mind, Parvati's forms include:
• Mahakali
• Sati
• Mahavidyas- Kali, Tara, Tripurasundari, Bhuvaneshwari, Bhairavi, Chinnamasta, Dhumavati, Bagalamukhi
• The Shakta pithas
• Navadurgas - Shailaputri, Brahmacharini, Chandraghanta, Kushmanda, Skandamata, Katyayani, Kaalratri, Mahagauri, Siddhidhatri
• Annapurna
• Kaushiki
• Durga
• Shitala
• Maheshwari
• Ardhanarishvara
• Vindhyavasini
• Bhramari
• Shakambhari
• Raktadantika
• Twarita
• In North India- Khodiyar, Bahuchara Mata, Naina Devi, Jwala etc.
• In Western India- Bhavani, Saptashrungi, Ekvira, Amba etc.
• In East India-Dakshina Kali, Kamakhya, Jagadhatri etc.
• In South India- Meenakshi, Vishalakshi, Kamakshi, Abhirami, Mookambika, Akilandeswari, Mariamman, Karumariamman etc.
All of these incarnations helped provide security to the world and even brought Shiva into the participation of worldly affairs.
Like Vishnu, his consort Lakshmi incarnates as in many forms to help provide order and to enlighten the world with her consort. She has many forms, and ju…

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