Please tell me chronological timeline (in Manvantara and Mahayuga) of Lord Vishnu's various incarnations.
Chapter 47 of Matsya Purana, Chapter 36 Part 2 of Vayu Purana, Chapter 19 of Prabhasa Khanda of Skanda Purana and Chapter 73 Upodgatapada of Brahmanda Purana mention timeline of Lord's some Avataras in Chronological order. These four Puranas mention same timeline. I will also mention from Bhagavata Purana.
In Sweta Varaha Kalpa (current Kalpa)
At beginning of Varaha Kalpa - Varaha Avatara. (Srimad Bhagavatam 3.13)
4th Treta Yuga of Vaivasvara Manvanatra - Narasimha Avatara to kill Hiranyakashipu (Chapter 47 of Matsya Purana and Chapter 36 of Vayu Purana)
7th Treta Yuga of Vaivasvara Manvantara - Vamana who appeared as Dwarf and seized Asuras with Bali to nether worlds.
10th Treta Yuga of Vaivasvara Manvantara - Dattatreya.
15th Treta Yuga of Vaivasra Manvantara - King Mandhata
19th Treta yuga of Vaivasvara - Parasurama to destroy evil Kshatriyas.
24th Treta Yuga of Vaivasvara - Ayodhya Rama to kill Ravana.
28th Dwapara yuga of Vaivasvara - Sri Krishna and Vedavyasa
28th Kali yuga of Vaivasvara - Buddha
End of 28th Kali Yuga of Vaivasvara - Kalki
Kurma and Varaha Purana don't mention exact times for Kurma and Varaha incarnations.
Please note that Lord Vishnu's incarnations are repetitive. So you may find more than one timeline for each incarnation. To understand this, let's read the below lines:
However there are very few sources but we can't ignore the story of Kakabhushundi. Kakabhushundi has seen Ramayana 11 times with different outcomes and seen Mahabharat 16 times with different results, but, after seeing Daksha Yagya twice, he did not either care to see it again or saw no point to seeing any more, as it ended the same way each time.
Also, few people believe in this as well:
Vasuki smiled and said, "This world we live in goes through cycles of life and death. In Treta Yuga, Ram takes birth. Then one day his ring falls into the subterranean realm of serpents through a tunnel. A monkey follows it and Ram on earth dies. So it has been for hundreds of thousands of times. All these rings testify to that fact.”
The order of these incarnation is as below, this can be related with modern day evolution theory as well. However, Mohini Incarnation (happened soon after Kurma incarnation during Samundra-Manthan) is an exception where modern day evolution theory fails :
In Sat Yuga : Varaha, Koorma, Matsya (Creatures that live in water/amphibian or live on land with swimming ability)
In Sat Yuga : Nrisimha (The half-lion and half-human – a stage between Homo sapiens and animals; killed Hirnyakashyap)
In Treta Yuga : Vamana (The Homo sapiens with short stature; sent Bali (great grandson of Hirnyakashyap) to Rasatal)
In Treta Yuga : Parasurama (The rough and tough human - Rama with the axe; killed Kartvirya Arjun (the king of Maheshmati) and then his army/descendants many time)
In Treta Yuga : Rama (Rama with a bow & noble practices; killed Ravana)
In Dwapara Yuga : Krishna (no explanation needed!)
Few timelines are as below but it doesn't mean there are no other timelines for these incarnations:
In the very beginning of Svet-Vrah kalp (present kalp) i.e. 1st Sat yuga of 1st Manvantar (ruled by Swayambhu Manu). Lord Varah restored the Earth in the beginning of this kalps, hence, the present kalp is named after Vishnu's this incarnation.
Note: this incarnation happened again to kill the asura Hirnaksh (brother of Hirnakashyap).
Koorma and Mohini Incarnation
Lord Vishnu took these incarnation during Samundra-Manthan (not sure about yuga but most of the sources says that Samundra-Manthan happened in previous manvantra i.e in the 6th or Chakshusha Manvantar of the Svet-Vrah or present kalp).
Note: Lord Vishnu took Mohini form again and Aiyappa was born.
At the end of 6th Manvantar (Cākṣuṣa-manvantara) or in the beginning (1st Sata yuga) of 7th Manvantar (Vaivaswata or present Manvantar) of the Svet-Vrah or present kalp. This incarnation of Vishnu saved Satayvrata from the deluge (Pralaya), who later became 7th Manu (Vaivaswata) and the current Manvantar is named after his name.
Note: This incarnation happened earlier as well to save Vedas from the demon Hayagrīva at the beginning of this Kalpa or at the end of previous Kalpa.
Parasurama and Rama Incarnation
In the Treta yugas of 7th Manvantar (Vaivaswata or present Manvantar) of the Svet-Vrah or present kalp.
Krishna, Krishńa Dwaipáyana and Balrama Incarnation
In the 28th Dwápara yuga which is recently passed (Dwápara yuga in which Krishńa Dwaipáyana holds the title of Ved Vyash) of 7th Manvantar (Vaivaswata or present Manvantar) of the Svet-Vrah or present kalp.
Note: Same is the time line for Krishńa Dwaipáyana (who is know as Vedvyasa, not considered in Dashavataram but in 24 incarnations) and Balrama(few people believe Balrama as Vishnu's incarnation and few as SheshNaga's incarnation).
In the 28th Kaliyuga yuga which is going on (around 500 BCE) of 7th Manvantar (Vaivaswata or present Manvantar) of the Svet-Vrah or present kalp.
Yet to happen in 28th Kaliyuga.
Synthesis of various avatars/incarnations using Laghu Bhagavatamrta.
- Narada and 4 Kumaras appeared in the first Kalpa and they stay throughout the life of Brahma. They are both avesavatara. (LB 3.7)
Present Kalpa / Sveta-varaha Kalpa / Brahma Kalpa
Svayambhuva Manvantara (First Manvantara)
- Lord Varaha deva came in black form to lift the earth which was inundated due to the curse of Agastaya Muni (LB 3.10)
- Lord Matsya came to kill Hayagriva and protect the vedas (LB 3.34)
- Lord Yajna comes to help the manu in managing the Universe (LB 3.37)
- Lord Nara-Narayana as offsprings of Dharma. (LB 3.38)
- Lord Dattatreya (LB 3.46)
- Lord Kapila as son of Kardama Muni teaching devotional service (LB 3.43)
- Lord Hayagriva appeared at Brahma's sacrifice and destroyed the demons Madhu & Kaitabha (LB 3.49-50)
- Lord Prsni-garbha (LB 3.54)
- King Rsabha (LB 3.58)
- King Prthu (LB 3.60)
- Lord Kurma in the beginning of the day to lift the Earth (LB 3.66)
- Lord Vamana deva took land form Vaskali (LB 3.73)
Caksusa Manvantara (6th Manvantara)
- Varaha deva, in a white form, came to kill Hiranyaksha and life the earth (LB 3.10) (May be 4th Yuga as per Vayu Purana Chapter 36)
- Lord Nrsimha appeared to protect Prahlad and kill Hiranyakashipu. (LB 3.64) (May be 4th Yuga as per Vayu Purana Chapter 36)
- Lord Kurma to hold up Mandara mountain while churning of the ocean. (LB 3.66)
- Lord Dhanvantari during the churning of the ocean. (LB 3.69)
- Lord Mohini to bewilder the demons during the churning of the ocean (3.70/71)
- Lord Matsya came to save king Satyavrata at the end of Caksusa (LB 3.34)
Vaivasvata Manvantara (7th Manvantara )
- Lord Dhanvantari also known as Dhanva as son of King of Kasi (LB 3.69)
- Lord Mohini to appease Siva (LB 3.70/71)
- Lord Vamana deva took land from king Dhun DHuna (LB 3.73) (Yuga unknown. However Lord Vamana deva came twice in this manvantara)
- Lord Vamana deva took land from Bali Maharaj in the seventh Treta yuga. (LB 3.73)
- Lord Parasurama came to kill the deviant Kshatriyas (17th or 22nd yuga acc to LB 3.75) (19th Yuga acc to Vayu P Ch 36)
- Lord Rama came to kill Ravana in the 24th Yuga cycle (Vayu P ch 36, LB 3.77)
- Lord Krishna in the 28th Dwapara Yuga (Vayu P Ch 36)
- Lord Balaram in the 28th Dwapara Yuga (Vayu P CH 36)
- Lord Krishna Dwaiyapana Vyasa in the 28th Dwapara Yuga
- Lord BHudha in the 28th Yuga cycle (LB 3.89)
- Lord Kalki in the 28th Yuga cycle. (LB 3.92)
- Lord Chaitanya in the 28th Yuga cycle (LB 1.2)
These are the Lila avatars (I missed few). Then there are also Manvantara avatars too for each of the Manvantaras (LB 4).
The Destroyer has a great answer. However, Puranas when they give dates it can become confusing to separate the Manvantara aspect. Thanks to Srila Rupa Goswami and Srila Baladeva Vidyabhusana, we have Laghu Bhagavatmrta. Below are the lists from various Puranas
Acc. to Matsya Purana (Ch 47)
- Narasimha dev in Satya Yuga
- Vamana dev in treta yuga
- King mandhatta in fifteenth treta yuga
- King parsurama in 19th treta yuga
- Lord Rama in 24th yuga
- Krtavirya born in 25th yuga
Acc. to Vayu Purna from 36th chapter as mentioned above.
- Rama avatara in 24th treta yuga
- Narsimha avatara in fourth yuga
- Vamana avatara in 7th Treta Yuga
- Dattatreya avatara in 10th treta yuga
- Mandhata avatara in 15th Treta yuga
- Parsurama avatara in 19th Treta yuga
Acc. to Brahmanda Purana (2.3.73)
- Dhruva in first treta yuga
- Rama in 24 yuga
- Varah in 4th yuga
- Dattatreya in 10th yuga
- Mandahatta in 15th
- Parsurama in 19th
Acc. to Padma Purana
- Rama in 24th yuga
- Parsurma in 12th yuga
- RAma in 27th (but not Dashrathi Rama)
Acc. to Devi Bhagavata Purana (4th book ch 16)
- Dattatreya in 2nd yuga
- Narasimha in 4th yuga
- Parsurama in 19th yuga