The incarnation of Lord Vishnu is mentioned in Hinduism
All the incarnations of Lord Vishnu are worshiped, among them the incarnation of Lord Rama and Shri Krishna is worshiped by many people and we get information about them from Ramayana and Srimad Bhagavad Gita.
Their 10 avatars are
1. Matsya Avatar:
According to the Puranas, Lord Vishnu had taken a matsyavatar to save the world from the Holocaust. Its story goes like this - King Satyavrat was born in the beginning of the era. King Satyavrat was giving Jalanjali a bath in the river one day. Suddenly a small fish came to his Anjali. When he saw it, I thought I would put it back in the ocean, but that fish said - Do not put me in the ocean, otherwise big fish will eat me. Then King Satyavrat kept the fish in his kamandal. When the fish became bigger, the king kept it in his lake, then on seeing it, the fish became bigger.
The king understood that this is not an ordinary creature. The king pleaded with the fish to come in real form. Hearing the king's prayer, the lord Vishnu appeared, and said that this is my mermaid. God told Satyavrat - listen King Satyavrat! There will be a catastrophe seven days from today. Then a huge boat will come to you with my inspiration. Take the subtle body of sapta sages, medicines, seeds and creatures and sit in it, when your boat starts to waver, then I will come to you as a fish. At that time you tie that boat with my horn by Vasuki Nag. At that time, I will answer you by asking questions, so that my glory, which is known as Parbrahma, will be revealed in your heart. Then, when the time came, the fishery god Vishnu preached philosophy to King Satyavrat, who is famous as Matsya Purana.
2. Kurma Avatar:
According to religious texts, Lord Vishnu had helped in churning the sea by taking the avatar of Kurma (turtle). The Kurma avatar of Lord Vishnu is also called the Kachhap avatar. Its story is as follows- Once Maharishi Durvasa cursed Indra, the king of the gods, to dehumanize him. When Indra went to Lord Vishnu, he asked him to churn the ocean. Then Indra agreed to churn the ocean together with the demons and deities as told by Lord Vishnu.
To churn the sea, the Mandarachal mountain was made a churner and Nagraj Vasuki was netted. The gods and the demons, forgetting their differences, uprooted Mandarachal and took him towards the sea, but they could not take him far. Then Lord Vishnu placed Mandarachal on the beach. The gods and demons made Mandarachal into the sea and made Nagaraja Vasuki a leader. But due to no base below Mandarachal, he started drowning in the sea. Seeing this, Lord Vishnu took the form of a giant kurma (turtle) and became the basis of Mandarachal in the sea. Mandarachal started moving fast on the huge back of Lord Kurma and thus the sea churning was completed.
3. Varaha Avatar:
According to religious texts, Lord Vishnu took the second incarnation as Varaha. The story related to the Varaha avatar is as follows - In ancient times when Lord Hiranyaksha carried the earth and hid it in the sea, then Lord Vishnu appeared in the form of Varaha from the nose of Brahma. Seeing this form of Lord Vishnu, all the gods and sages praised him. At the urging of everyone, Lord Varaha started searching for the earth. With the help of his snout, he found the earth and by going inside the ocean and placing it on his teeth, he brought the earth out.
When Hiranyaksha demon saw this, he challenged the Varaha form of Lord Vishnu to battle. A fierce battle ensued in both. Finally Lord Varaha killed Hiranyaksha. After this, Lord Varaha pillaged the water with his hooves and set the earth on it.
4. Lord Narasimha:
Lord Vishnu had killed Narasimha incarnation of Hiranyakashipu, the king of the demons. The story of this incarnation is as follows- According to religious texts, Hiranyakashipu, the king of the demons, considered himself stronger than God. He had the gift of dying from man, god, bird, animal, neither in day, nor at night, nor on earth, nor in the sky, nor by weapon, nor by weapon. Whoever worshiped Lord Vishnu during his reign was punished. His son's name was Prahlad. Prahlada was an ardent devotee of Lord Vishnu since childhood. When Hiranyakashipu came to know about this, he was very angry and tried to convince Prahlada, but even when Prahlada did not believe Hiranyakashipu gave him the death penalty.
Every time he survived the miracle of Lord Vishnu. Hiranyakashipu's sister Holika, who had the boon of not burning with fire, sat in a blazing fire with Prahlada. Even then, by the grace of Lord Vishnu Prahlad survived and Holika was burnt. When Hiranyakashipu was about to kill Prahlad himself, Lord Vishnu appeared from the pillar with the incarnation of Narasimha and killed Hiranyakashipu with his nails.
5. Vamana Avatar:
In Satyayuga, Prahlada's grandson, Daityaraj Bali, took control of heaven. All the gods went to Lord Vishnu to avoid this calamity. Then Lord Vishnu said that I myself will be born from the womb of Devmata Aditi and will give you the kingdom of heaven. After some time Lord Vishnu incarnated Vamana.
Once, when Bali was performing a great yajna, Lord Vaman went to the sacrificial fire and asked for three feet of land from King Bali. Shukracharya, the Guru of King Bali, understood the lila of God and refused to donate to Bali. But Bali still pledged to donate three feet of land to Lord Vamana. Lord Vamana took a huge form and measured the earth in one step and the heaven in the second step. When there was no place left for the third step, Bali sacrificed God Vamana on his head.
6. Shriram avatar:
The demon king Ravana had great terror in Tretayuga. Gods were also afraid of him. For his slaughter, Lord Vishnu was born as a son from the womb of Mother Kaushalya at King Dasharatha. In this incarnation, Lord Vishnu killed many demons and lived his life by following Maryada.
Went to exile at the behest of father. While suffering exile, Raksharaj Raja took away his wife Sita. In search of Sita, Lord reached Lanka, where there was a fierce battle between Lord Rama and Ravana in which Ravana was killed. Thus Lord Vishnu took the Rama avatar and freed the gods.
7. Shri Krishna Avatar:
In Dwaparyug, Lord Vishnu took the Shri Krishna incarnation and destroyed the unrighteous. Lord Krishna was born in a prison. His father's name was Vasudev and mother's name was Devaki. Lord Krishna performed many miracles in this incarnation and annihilated the wicked.
Lord Krishna also killed Kansa. In the war of Mahabharata, became the charioteer of Arjuna and gave the knowledge of Gita to the world. Dharmaraja established Dharma by making Yudhishthira king. This incarnation of Lord Vishnu is considered the best of all incarnations.
8. Parashuram Avatar:
According to Hindu scriptures, Parashurama was one of the major incarnations of Lord Vishnu. There are two stories regarding the birth of Lord Parashurama. According to Harivanshpuran, one of those stories is as follows:
In ancient times, the city of Mahishmati was ruled by the powerful Haiyavanshi Kshatriya Kartavirya Arjuna (Sahastrabahu). He was very arrogant and also tyrannical. Once Agnidev requested him to take food. Then Sahastrabahu came in boasting and said that you can get food from wherever you want, I rule all around. Then Agnidev started burning forests. In a forest, the sage Aapava was doing penance. Agni also burnt his ashram. Enraged by this, the sage cursed Sahastrabahu that Lord Vishnu would be born as Parashurama and destroy not only Sahastrabahu but all the Kshatriyas. Thus Lord Vishnu was born as the fifth son of Maharishi Jamadagri in the Bhargava clan.
9. Buddha avatar:
According to religious texts, Gautama Buddha, the originator of Buddhism, was also an incarnation of Lord Vishnu, but Lord Buddha, described in the Puranas, is said to have been born in Kikat near Gaya and his father's name is said to be Ajna. This passage is of the Buddhavatar mentioned in the Puranas.
At one time the power of the demons increased greatly. The gods also started running away from their fear. With the wish of the kingdom, the demons asked Devraj Indra that our empire should remain stable, what is the solution for this. Then Indra told with a pure sense that Yajna and Vedic conduct is necessary for stable governance. Then the demons started performing Vedic conduct and Mahayagya, which further increased their power. Then all the gods went to Lord Vishnu. Then Lord Vishnu took the form of Buddha for the benefit of the gods. They had a market in their hands and they walked along the path.
Thus Lord Buddha approached the demons and preached to them that sacrificing yagna is a sin. Yajna causes life violence. Many beings are consumed by the fire of sacrifice. The demons were impressed by the teachings of Lord Buddha. He stopped performing Yajna and Vedic conduct. This reduced his power and the gods attacked him and regained his kingdom.
10. Kalki Avatar:
According to religious texts, Lord Vishnu will incarnate in Kalki form in Kali Yuga. Kalki avatar will be in the jurisdiction of Kali Yuga and Satyuga. This avatar will consist of 64 arts. According to the Puranas, Lord Kalki will be born as a son of an ascetic Brahmin named Vishnuyasha at a place called Shambhal in Moradabad district of Uttar Pradesh. Riding on a horse named Kalki Devadatta will destroy the sinners from the world and re-establish religion, only then will the beginning of the golden age begin.