1. Matsya (Fish – Satya Yuga)
Matsya was the first avatar of the god Vishnu in the form of a fish. In the Matsya avatar, Lord Vishnu described to have rescued the first man, Vaivasvata Manu, the seven sages at the time of great Flood (massive cyclone) where he took his boat to the new world with one of every species of plant and animal.
Matsya is depicted as a giant fish, or anthropomorphically with a half-human torso connected to the rear half of a fish.
2. Kurma (Tortoise – Satya Yuga)
Kurma (Koorma) was the second avatar of the Lord Vishnu in the form of a tortoise. When the devas and asuras (demons) were churning the Ocean of milk in order to get Amrita (the nectar of immortality), the mount Mandara they were using as the churning staff started to sink and God Vishnu took the form of a tortoise to hold the weight of the mountain.
3. Varaha (Boar – Satya Yuga)
Varaha was the third avatar of the God Vishnu in the form of a boar. When the demon Hiranyaksha stole the earth (personified as the goddess Bhudevi) and hid her in the primordial waters, Lord Vishnu appeared as Varaha to rescue her. Varaha slew the demon and retrieved the Earth from the ocean, lifting it on his tusks, and restored Bhudevi to her place in the universe.
4. Narasimha (Half-man/half-lion – Satya Yuga)
Narasimha was the fourth avatar of the God Vishnu in the form of a half-man/half-lion. The rakshasa (demon) Hiranyakashipu was granted a powerful boon from the lord brahma, not allowing him to be killed by man or animal, inside or out, day or night, on earth or the stars, with a weapon either living or inanimate.
Lord Vishnu descended as an anthropomorphic incarnation, with the body of a man and head and claws of a lion. He then disembowels the rakshasa at the courtyard threshold of his house, at dusk, with his claws, while he lay on his thighs.
5. Vamana (Dwarf – Treta Yuga)
Vamana was the fifth avatar of the Lord Vishnu in the form of a dwarf man. This is the first avatar to appear as a human, carrying a wooden umbrella. Lord Vishnu descended as the Vamana avatar to restore the authority of Indra over the heavens. Vamana went to the king Mahabali to request three paces of land and the king consented against his guru Sukracharya‘s wishes.
Vamana then revealed his true identity and enlarged into gigantic proportions to stride over the three worlds. He stepped from heaven to earth with the first step and from earth to the netherworld with the second step. King Mahabali was unable to fulfill his promise, offered his head for the third. Vamana then placed his foot and gave the king immortality for his humility.
6. Parashurama (Warrior with an Axe – Treta Yuga)
Parashurama was the sixth avatar of Lord Vishnu. Parashuram was son of Jamadagni and Renuka and received an axe after a penance to Lord Shiva. He was the first Brahmin & Kshatriya in Hinduism (i.e, warrior-saint) with duties between a Brahmin and a Kshatriya. King Kartavirya Arjuna and his army visited the father of Parashurama at his ashram, and the saint was able to feed them with the divine cow Kamadhenu.
The king demanded the cow, but Jamadagni refused. The enraged king took it by force and destroyed the ashram. Parashurama then killed the king at his palace and destroyed his army single-handedly. In revenge, the sons of Kartavirya killed Jamadagni. Parashurama took a vow to kill every Kshatriya on earth twenty-one times over, and filled five lakes with their blood. Ultimately, his grandfather, rishi Rucheeka, appeared before him and made him halt. Parashuram is considered a Chiranjivi (i.e., immortal), and believed to be alive today in penance at Mahendragiri mountain.
7. Rama (Prince/king of Ayodhya – Treta Yuga)
Rama was the seventh avatar of God Vishnu. Lord Rama is a commonly worshiped avatar in Hinduism, and is thought of as the ideal heroic man. His story is one of the most widely read scriptures of Hinduism, the Ramayana.
While in exile from his own kingdom with his brother Lakshman for 14 years and the God Hanuman, his wife Sita was abducted by the demon king of Sri Lanka, Ravana. He then traveled to Ashoka Vatika (or vanam) in Lanka, killed the demon king and saved Sita.
8. Krishna (Philosopher & Guide – Dwapara Yuga)
Krishna was the ninth avatar of Lord Vishnu. Lord Krishna was the eighth son of Devaki and Vasudev. He is widely worshiped deity in Hinduism and an avatar in Vaishnava belief. He appeared alongside his elder brother Balarama. Balarama is regarded generally as an avatar of Lord Vishnu.
However Balarama is included as the eighth avatar of Vishnu in the Sri Vaishnava lists, where Buddha is omitted and Krishna appears as the ninth avatar in this list.
9. Venkateswara– (Kali Yuga)
Krishna is the 8th avatar and after him, they believe Lord Venkateshwara (Balaji) to be the 9th avatar. Since Buddha created a whole new religion which kind of goes against the teachings of Krishna and Rama, so they do not believe Buddha is a part of Hinduism or Lord Vishnu at all.
Hathirama Babaji was one of Lord Vishnu's biggest devotees. When he got to know that Vishnu in present in Tirupati as Lord Venkateshwara, he came all the way to Tirupati from north India. When he arrived, it was late and the priests didn't let him in. So he decided to commit suicide by jumping from the top of a hill
10. Kalki (Eternity/White-Horse – Kali Yuga)
In Hinduism, Kalki (meaning destroyer of evil) will be the tenth avatar of the god Vishnu, foretold to appear at the end of Kali Yuga. The Purana scriptures foretell that Kalki will be atop a white horse with a drawn blazing sword. He will be the harbinger of the end time in Hindu eschatology, after which he will usher into Satya Yuga.