The ten primary incarnations (Avatars) of Vishnu, known as the Dashavatara, are:
1. Matsya (The Fish): Vishnu incarnates as a fish to save Manu (the progenitor of mankind) and the sacred scriptures from a great flood.
2. Kurma (The Tortoise): Vishnu becomes a tortoise to support Mount Mandara during the churning of the ocean of milk (Samudra Manthan) by the gods and demons to obtain the elixir of immortality (Amrita).
3. Varaha (The Boar): Vishnu takes the form of a boar to defeat the demon Hiranyaksha, who had dragged the Earth (represented as the goddess Bhumi) to the bottom of the cosmic ocean, and to restore the Earth to its rightful place.
4. Narasimha (The Man-Lion): Vishnu appears as a half-man, half-lion to kill the demon Hiranyakashipu, who had received a boon that made him virtually invincible. Narasimha appears at twilight, neither day nor night, on the threshold of a doorway, neither inside nor outside, and kills Hiranyakashipu with his claws, not any weapon.
5. Vamana (The Dwarf): Vishnu incarnates as a dwarf Brahmin to humble the benevolent demon king Bali. Vamana asks Bali for three paces of land. Bali grants the request, and Vamana grows to an enormous size, covering the earth in one step, the heavens in the second, and asks Bali where to place his third foot. Bali offers his own head in humility, thus fulfilling the promise.
6. Parashurama (The Axe-Wielding Warrior): Vishnu is born as a Brahmin warrior with an axe to rid the world of the tyrannical Kshatriya (warrior) class, who were abusing their power.
7. Rama (The Righteous King): Vishnu incarnates as Rama, the prince of Ayodhya, to defeat the demon king Ravana and establish dharma (righteousness). His story is famously told in the epic Ramayana.
8. Krishna (The Divine Statesman): Vishnu appears as Krishna, a wise and powerful prince, to rid the world of evil and deliver the Bhagavad Gita, a sacred scripture containing profound philosophical teachings. He plays a key role in the epic Mahabharata.
9. Buddha (The Enlightened One): This is a controversial incarnation, as interpretations differ. Some consider the Buddha as an avatar of Vishnu who came to end animal sacrifices and lead people away from Vedic rituals. Others, particularly Buddhists, do not accept this view.
10. Kalki (The Destroyer): Kalki is the prophesied final avatar of Vishnu, who is expected to appear at the end of the Kali Yuga (the current epoch) to destroy evil and usher in a new cycle of righteousness (Satya Yuga). He is often depicted as a warrior riding a white horse with a flaming sword.
It's important to note that the order and even the inclusion of Buddha as an avatar can vary depending on the specific tradition or school of thought within Hinduism.