The ten Avaters
In Hinduism, an avatar from Sanskrit "descent") is a deliberate descent of a deity to Earth, or a descent of the Supreme Being (e.g., Vishnu for Vaishnavites), and is mostly translated into English as "incarnation", but more accurately as "appearance" or "manifestation".
The phenomenon of an avatar is observed in Hinduism, Ayyavazhi, and Sikhism. Avatar is regarded as one of the core principles of Hinduism.
The term is most often associated with Vishnu, though it has also come to be associated with other deities Varying lists of avatars of Vishnu appear in Hindu scriptures, including the ten Dashavatara of the Garuda Purana and the twenty-two avatars in the Bhagavata Purana, though the latter adds that the incarnations of Vishnu are innumerable. The avatars of Vishnu are a primary component of Vaishnavism. An early reference to avatar, and to avatar doctrine, is in the Bhagavad Gita.
Shiva and Ganesha are also described as descending in the form of avatars. The various manifestations of Devi, the Divine Mother principal in Hinduism, are also described as avatars or incarnations by some scholars and followers ofShaktism. The avatars of Vishnu carry a greater theological prominence than those of other deities, which some scholars perceive to be imitative of the Vishnu avatar lists.
In Sikhism, an avatar is a deliberate descent of a soul to earth in any form. Guru Granth Sahib believes in the existence of the Dashavatara. In Dasam Granth, Guru Gobind Singh wrote three composition on historical avatars which include Vishnu Avatar, Brahma Avatar, and Rudra Avatar.

Ten avatars of Vishnu (Matsya, Kurma,Varaha, Vamana, Krishna, Kalki, Buddha,Parshurama, Rama & Narasimha). Painting from jaipur, now at the Victoria and Albert Museum

The Garuda
The Garuda is a large bird-like creature, or humanoid bird that appears in both Hinduism and Buddhism. Garuda is themount (vahana) of the Lord Vishnu. Garuda is the Hindu name for the constellation Aquila. The brahminy kite andphoenix are considered to be the contemporary representations of Garuda.Indonesia adopt a more stylistic approach to the Garuda's depiction as its national symbol, where it depicts a Javanese eagle (being much larger than akite).
In Hinduism, Garuda is a Hindu divinity, usually the mount (vahana) of the Lord Vishnu. Garuda is depicted as having the golden body of a strong man with a white face, red wings, and an eagle's beak and with a crown on his head. This ancient deity was said to be massive, large enough to block out the sun.
Garuda is known as the eternal sworn enemy of the Nāga serpent race and known for feeding exclusively on snakes, such behavior may have referred to the actual short-toed eagle of India. The image of Garuda is often used as the charm oramulet to protect the bearer from snake attack and its poison, since the king of birds is an implacable enemy and "devourer of serpent". Garudi Vidya is the mantra against snake poison to remove all kinds of evil.
His stature in Hindu religion can be gauged by the fact that a dependent Upanishad, the Garudopanishad, and a Purana, theGaruda Purana, is devoted to him. Various names have been attributed to Garuda - Chirada, Gaganeshvara, Kamayusha, Kashyapi, Khageshvara, Nagantaka, Sitanana, Sudhahara, Suparna, Tarkshya, Vainateya, Vishnuratha and others. TheVedas provide the earliest reference of Garuda, though by the name of Shyena, where this mighty bird is said to have broughtnectar to earth from heaven. The Puranas, which came into existence much later, mention Garuda as doing the same thing, which indicates that Syena (Sanskrit for eagle) and Garuda are the same. One of the faces of Srī Pancamukha Hanuman is Mahavira Garuda. This face points towards the west. Worship of Garuda is believed to remove the effects of poisons from one's body. In Tamil Vaishnavism Garuda and Hanuman are known as "Periya Thiruvadi" and "Siriya Thiruvadi" respectively.
In the Bhagavad-Gita in the middle of the battlefield "Kurukshetra", Krishna explaining his omnipresence, says - “as son of Vinata, I am in the form of Garuda, the king of the bird community (Garuda)" indicating the importance of Garuda.
Garuda wears the serpent Adisesha on his left small toenail and the serpent Gulika on his right cerebral cortex. The serpent Vasuki forms his sacred thread. The cobra Takshaka forms his belt on his hip. The snake Karkotaka is worn as his necklace. The snakes Padma and Mahapadma are his ear rings. The snake Shankachuda adorns his divine hair. He is flanked by his two wives ‘Rudra’ and ‘Sukeerthi’ or (Sukirthi). These are all invoked in Vedanta Desika's Garuda Panchashath and Garuda Dandaka compositions. Garuda flanked with his consorts 'Rudra' and 'Sukirthi' can be seen worshipped in an ancient Soumya Keshava temple in Bindiganavile (or Mayura puri in Sanskrit ) in Karnataka state of India.