this is a matter compiled from various source.

Dashavatara 

The ten avatars of Vishnu of the Hindu God of universal preservation.

God Vishnu incarnates on Earth from time to time to eradicate evil forces, to restore the Dharma and to liberate the worthy ones / devotees from the cycle of births and deaths.

Matsyavatar 1

1. Matsya, the fish. Lord Vishnu takes the form of a fish to save Manu from apocalypse (destruction of the world), after which he takes his boat to the new world along with one of every species of plant and animal, gathered in a massive cyclone.

Shri Vishnu as Tortoise- Kurma

shri Vishnu bearing the wieght of the mountain

2. Kurma, the tortoise. When the devas and asuras were churning the Ocean of milk in order to get Amrit( the nectar of immortality) the mount Mandara they were using as the churning staff started to sink and Lord Vishnu took the form of a tortoise to bear the weight of the mountain.

Sri Vishnu as Varaha

3. Varaha, the boar. He appeared to defeat Hiranyaksha, a demon who had taken the Earth and carried it to the bottom of what is described as the cosmic ocean. Varaha carried the Earth out of the ocean between his tusks and restored it to its place in the universe.

Narsinha Avatar

4. Narasimha, the half-man/half-lion. The rakshasa Hiranyakashipu, the elder brother of Hiranyaksha, was granted a powerful boon from 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. 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.

Vaman Avatar

5. Vamana, the dwarf. The fourth descendant of Hiranyakashyap, Bali, with devotion and penance was able to defeat Indra, the god of firmament and extended his authority over the three worlds. Lord Vishnu descended as the dwarf Vamana. Vamana asked for three paces of land during a yajna of the king amidst other Brahmins. Bali agreed, and the dwarf then changed his size to that of a giant. He stepped over heaven in his first stride, and the netherworld with the second. Bali realized that Vamana was Vishnu incarnate. He offered his head as the third place for Vamana to place his foot. The avatar did so and thus granted Bali immortality. Then in appreciation to Bali and his grandfather Prahlada, Vamana made him ruler of Patal lok, the netherworld. Bali is believed to have ruled Kerala and Tulunadu. He is still worshiped there as the king of prosperity and recalled before the time of harvest.

Shri Parshuram

6. Parashurama, warrior with the axe. He is son of Jamadagni Rishi and Renuka. He received an axe after a penance to Shiva. Parashurama is the first Brahmin-Kshatriya in Hinduism a warrior-saint, with duties between a Brahmana and a Kshatriya. His mother was from the Kshatriya Suryavanshi clan that ruled Ayodhya, of the line of Rama. 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 animal, Jamadagni refused, and the king took it by force and destroyed the ashram. Parashurama then killed the king at his palace and destroyed his army. In revenge, the sons of Kartavirya killed Jamadagni. Parashurama took a vow to kill every Kshatriya on earth twenty-one times over,(as his mother renuka beats her chest twentyone times after seeing her husband). Ultimately, his grandfather, the great rishi Rucheeka, appeared and made him halt. He is a Chiranjivi, and believed to be alive today in penance at Mahendragiri in Tamilnadu.

Shri Ram

7. Rama, Ramachandra, the prince and king of Ayodhya. Rama was a heroic man. His story is recounted in one of the most widely read scriptures of Hinduism, the Ramayana. While in exile from his own kingdom with his brother Lakshman, his wife Sita was abducted by the demon king of Lanka, Ravana. He travelled to Ashoka Vatika in Lanka, killed the demon king and saved Sita.

Shri Krishna

8. Krishna was the eighth son of Devaki and Vasudev. Krishna is the most commonly worshiped deity in Hinduism and an avatar in Vaishnava belief. He appeared in the Dwapara Yuga alongside his brother Balarama. Balarama is the elder brother of Krishna and is an avatar of Sheshanag. 

Gautam Buddha

9. Buddha: Gautama Buddha, the founder of Buddhism, is generally included as an avatar of Vishnu in Hinduism. Buddha may be depicted in Hindu scriptures as a preacher who deludes and leads demons and heretics away from the path of the Vedic scriptures. Another view praises them as a compassionate teacher who preached the path of ahimsa (non-violence).

Kalki Avatara

10. Kalki ("Eternity", or "White Horse", or "Destroyer of Filth"), is the final incarnation of Vishnu, foretold to appear at the end of Kali Yuga, our present epoch. He will be atop a white horse and his sword will be drawn, blazing like a comet. He is the harbinger of end time in Hindu eschatology, and will destroy all unrighteousness and evil at the end of Kali Yuga.